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Algebras and representation theory
| Algebras and representation theory |
| Pubbl/distr/stampa | [Dordrecht], : Kluwer Academic Publishers |
| Descrizione fisica | 1 online resource |
| Disciplina | 512.4 |
| Soggetto topico |
Rings (Algebra)
Representations of algebras Representations of rings (Algebra) Anneaux (Algèbre) Représentations des algèbres Représentations d'anneaux (Algèbre) |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1572-9079 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910142802203321 |
| [Dordrecht], : Kluwer Academic Publishers | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Algebras and representation theory
| Algebras and representation theory |
| Pubbl/distr/stampa | [Dordrecht], : Kluwer Academic Publishers |
| Descrizione fisica | 1 online resource |
| Disciplina | 512.4 |
| Soggetto topico |
Rings (Algebra)
Representations of algebras Representations of rings (Algebra) Anneaux (Algèbre) Représentations des algèbres Représentations d'anneaux (Algèbre) |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1572-9079 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996208335203316 |
| [Dordrecht], : Kluwer Academic Publishers | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer
| Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer |
| Autore | Meltzer Hagen |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 514.224 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Vector bundles
Representations of rings (Algebra) Homology theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0409-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Background""; ""Chapter 2. Summary""; ""Chapter 3. Weighted projective lines""; ""3.1. Basic notations""; ""3.2. Exceptional sheaves""; ""3.3. Perpendicular categories""; ""Chapter 4. Mutations of exceptional sequences""; ""4.1. Exceptional sequences""; ""4.2. The braid group action on the set of exceptional sequences""; ""4.3. Transitivity of the braid group action""; ""4.4. Bijections between exceptional sheaves""; ""4.5. Coprimeness of rank and degree""; ""Chapter 5. Tubular mutations""
""5.1. Mutations as derived equivalences for sheaves on weighted projective lines of genus one""""5.2. Telescopic functors""; ""5.3. Automorphisms of the derived category""; ""Chapter 6. Twisted mutations""; ""6.1. Admissible exceptional pairs""; ""6.2. Twisted mutations of admissible exceptional pairs""; ""Chapter 7. On the number of exceptional vector bundles""; ""7.1. Equations and inequalities for exceptional bundles""; ""7.2. A bound for the number of exceptional bundles of fixed rank and degree""; ""7.3. Omnipresent exceptional vector bundles""; ""Chapter 8. Tilting sheaves"" ""8.1. Concealed�canonical and almost concealed�canonical algebras""""8.2. Regular components""; ""8.3. The wing decomposition of a tilting bundle""; ""8.4. Non�regular components for concealed�canonical algebras""; ""8.5. Non�regular components for almost concealed�canonical algebras""; ""Chapter 9. Tilting complexes""; ""9.1. Tilting complexes and exceptional sequences""; ""9.2. Tilting complexes for weighted projective lines with parameters""; ""9.3. Branch enlargements of concealed�canonical algebras""; ""9.4. Tilting complexes for domestic weighted projective lines"" ""9.5. Tilting complexes for tubular weighted projective lines""""Chapter 10. Hyperelliptic weighted projective lines""; ""10.1. Structure of a tilting complex on a hyperelliptic weighted projective line""; ""10.2. Diophantine equations""; ""10.3. Layered algebras""; ""10.4. Tame algebras derived equivalent to hyperelliptic algebras""; ""10.5. Tame algebras derived equivalent to t�subspace problem algebras""; ""10.6. Proofs of the classification results""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910480408003321 |
Meltzer Hagen
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer
| Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer |
| Autore | Meltzer Hagen |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 514.224 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Vector bundles
Representations of rings (Algebra) Homology theory |
| ISBN | 1-4704-0409-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Background""; ""Chapter 2. Summary""; ""Chapter 3. Weighted projective lines""; ""3.1. Basic notations""; ""3.2. Exceptional sheaves""; ""3.3. Perpendicular categories""; ""Chapter 4. Mutations of exceptional sequences""; ""4.1. Exceptional sequences""; ""4.2. The braid group action on the set of exceptional sequences""; ""4.3. Transitivity of the braid group action""; ""4.4. Bijections between exceptional sheaves""; ""4.5. Coprimeness of rank and degree""; ""Chapter 5. Tubular mutations""
""5.1. Mutations as derived equivalences for sheaves on weighted projective lines of genus one""""5.2. Telescopic functors""; ""5.3. Automorphisms of the derived category""; ""Chapter 6. Twisted mutations""; ""6.1. Admissible exceptional pairs""; ""6.2. Twisted mutations of admissible exceptional pairs""; ""Chapter 7. On the number of exceptional vector bundles""; ""7.1. Equations and inequalities for exceptional bundles""; ""7.2. A bound for the number of exceptional bundles of fixed rank and degree""; ""7.3. Omnipresent exceptional vector bundles""; ""Chapter 8. Tilting sheaves"" ""8.1. Concealed�canonical and almost concealed�canonical algebras""""8.2. Regular components""; ""8.3. The wing decomposition of a tilting bundle""; ""8.4. Non�regular components for concealed�canonical algebras""; ""8.5. Non�regular components for almost concealed�canonical algebras""; ""Chapter 9. Tilting complexes""; ""9.1. Tilting complexes and exceptional sequences""; ""9.2. Tilting complexes for weighted projective lines with parameters""; ""9.3. Branch enlargements of concealed�canonical algebras""; ""9.4. Tilting complexes for domestic weighted projective lines"" ""9.5. Tilting complexes for tubular weighted projective lines""""Chapter 10. Hyperelliptic weighted projective lines""; ""10.1. Structure of a tilting complex on a hyperelliptic weighted projective line""; ""10.2. Diophantine equations""; ""10.3. Layered algebras""; ""10.4. Tame algebras derived equivalent to hyperelliptic algebras""; ""10.5. Tame algebras derived equivalent to t�subspace problem algebras""; ""10.6. Proofs of the classification results""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910788747503321 |
|
Meltzer Hagen
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer
| Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer |
| Autore | Meltzer Hagen |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 514.224 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Vector bundles
Representations of rings (Algebra) Homology theory |
| ISBN | 1-4704-0409-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Background""; ""Chapter 2. Summary""; ""Chapter 3. Weighted projective lines""; ""3.1. Basic notations""; ""3.2. Exceptional sheaves""; ""3.3. Perpendicular categories""; ""Chapter 4. Mutations of exceptional sequences""; ""4.1. Exceptional sequences""; ""4.2. The braid group action on the set of exceptional sequences""; ""4.3. Transitivity of the braid group action""; ""4.4. Bijections between exceptional sheaves""; ""4.5. Coprimeness of rank and degree""; ""Chapter 5. Tubular mutations""
""5.1. Mutations as derived equivalences for sheaves on weighted projective lines of genus one""""5.2. Telescopic functors""; ""5.3. Automorphisms of the derived category""; ""Chapter 6. Twisted mutations""; ""6.1. Admissible exceptional pairs""; ""6.2. Twisted mutations of admissible exceptional pairs""; ""Chapter 7. On the number of exceptional vector bundles""; ""7.1. Equations and inequalities for exceptional bundles""; ""7.2. A bound for the number of exceptional bundles of fixed rank and degree""; ""7.3. Omnipresent exceptional vector bundles""; ""Chapter 8. Tilting sheaves"" ""8.1. Concealed�canonical and almost concealed�canonical algebras""""8.2. Regular components""; ""8.3. The wing decomposition of a tilting bundle""; ""8.4. Non�regular components for concealed�canonical algebras""; ""8.5. Non�regular components for almost concealed�canonical algebras""; ""Chapter 9. Tilting complexes""; ""9.1. Tilting complexes and exceptional sequences""; ""9.2. Tilting complexes for weighted projective lines with parameters""; ""9.3. Branch enlargements of concealed�canonical algebras""; ""9.4. Tilting complexes for domestic weighted projective lines"" ""9.5. Tilting complexes for tubular weighted projective lines""""Chapter 10. Hyperelliptic weighted projective lines""; ""10.1. Structure of a tilting complex on a hyperelliptic weighted projective line""; ""10.2. Diophantine equations""; ""10.3. Layered algebras""; ""10.4. Tame algebras derived equivalent to hyperelliptic algebras""; ""10.5. Tame algebras derived equivalent to t�subspace problem algebras""; ""10.6. Proofs of the classification results""; ""Bibliography""; ""Index"" |
| Record Nr. | UNINA-9910807397503321 |
|
Meltzer Hagen
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Expository lectures on representation theory : Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA / / Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors
| Expository lectures on representation theory : Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA / / Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| Descrizione fisica | 1 online resource (236 p.) |
| Disciplina | 512/.46 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Associative rings
Representations of rings (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1441-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Preface""; ""Fine and coarse moduli spaces in the representation theory of finite dimensional algebras""; ""1. Introduction and notation""; ""Acknowledgements""; ""2. Affine and projective parametrizations of the Î?-modules of dimension vector ""; ""3. Quotient varieties on the geometric marketâ€?generalities and representation-theoretic particulars""; ""4. Rendering Riemannâ€?s classification philosophy more concrete""; ""5. Approach A: Kingâ€?s adaptation of Mumford stability: Focusing on the objects which are (semi-)stable relative to a weight function""
""6. Approach B. Slicing Î?- into strata with fixed top""""7. Slicing Î?- more finely, in terms of radical layerings Representation-theoretically optimal coordinatization of ^{ }_{ }""; ""8. Problems. Pros and Cons of Approach B""; ""References""; ""More Representations of Wild Quivers""; ""Introduction""; ""1. Preliminaries""; ""2. Spectral properties of the Coxeter transformations""; ""3. Elementary modules""; ""4. The regular components""; ""5. Partial tilting modules""; ""6. The perpendicular category of a rigid regular module"" ""7. A functor between categories of regular modules""""8. Generation of cocones""; ""9. Factorisations of morphisms""; ""References""; ""Phantom Morphisms and Salceâ€?s Lemma""; ""1. Introduction""; ""2. Preliminaries""; ""3. Salceâ€?s Lemma""; ""4. The Flat Cover Conjecture""; ""5. Phantom Morphisms""; ""6. Salceâ€?s Lemma for Ideals""; ""7. Subfunctors of ""; ""8. Examples""; ""9. Quasi-Frobenius Rings""; ""10. The Powers of the Phantom Ideal""; ""References""; ""Morita theory, revisited""; ""1. Introduction""; ""2. Notations""; ""3. Morita theory""; ""4. The Lambek theorem"" ""5. Self-dual idempotents and Morita algebras""""References""; ""Universal deformation rings of group representations, with an application of Brauerâ€?s generalized decomposition numbers""; ""1. Introduction""; ""2. Mazurâ€?s deformation theory""; ""3. Universal deformation rings of modules for finite groups""; ""4. Brauerâ€?s generalized decomposition numbers and universal deformation rings""; ""References""; ""Derived Representation Schemes and Noncommutative Geometry""; ""1. Introduction""; ""Notation and Conventions""; ""2. Model categories""; ""3. Representation Schemes"" ""4. Cyclic Homology and Higher Trace Maps""""5. Abelianization of the Representation Functor""; ""6. Examples""; ""Acknowledgements""; ""References""; ""Classifying torsion pairs for tame hereditary algebras and tubes""; ""Introduction""; ""1. Torsion pairs""; ""2. Torsion pairs and tilting for finite dimensional algebras""; ""3. Big cotilting modules for finite dimensional algebras""; ""4. Tubes""; ""5. Combinatorial classifications""; ""References""; ""Problems solved by using degrees of irreducible morphisms""; ""Introduction""; ""1. Preliminaries and Notation""; ""2. On degrees"" ""3. Characterizations of the notion of degree"" |
| Record Nr. | UNINA-9910479985603321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Expository lectures on representation theory : Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA / / Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors
| Expository lectures on representation theory : Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA / / Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| Descrizione fisica | 1 online resource (236 p.) |
| Disciplina | 512/.46 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Associative rings
Representations of rings (Algebra) |
| ISBN | 1-4704-1441-4 |
| Classificazione | 16G1016G2016G6016G7020C2016W2514L30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Fine and coarse moduli spaces in the representation theory of finite dimensional algebras -- 1. Introduction and notation -- Acknowledgements -- 2. Affine and projective parametrizations of the Î?-modules of dimension vector -- 3. Quotient varieties on the geometric market"generalities and representation-theoretic particulars -- 4. Rendering Riemann's classification philosophy more concrete -- 5. Approach A: King's adaptation of Mumford stability: Focusing on the objects which are (semi-)stable relative to a weight function -- 6. Approach B. Slicing Î?- into strata with fixed top -- 7. Slicing Î?- more finely, in terms of radical layerings Representation-theoretically optimal coordinatization of ^{ }_{ } -- 8. Problems. Pros and Cons of Approach B -- References -- More Representations of Wild Quivers -- Introduction -- 1. Preliminaries -- 2. Spectral properties of the Coxeter transformations -- 3. Elementary modules -- 4. The regular components -- 5. Partial tilting modules -- 6. The perpendicular category of a rigid regular module -- 7. A functor between categories of regular modules -- 8. Generation of cocones -- 9. Factorisations of morphisms -- References -- Phantom Morphisms and Salce's Lemma -- 1. Introduction -- 2. Preliminaries -- 3. Salce's Lemma -- 4. The Flat Cover Conjecture -- 5. Phantom Morphisms -- 6. Salce's Lemma for Ideals -- 7. Subfunctors of -- 8. Examples -- 9. Quasi-Frobenius Rings -- 10. The Powers of the Phantom Ideal -- References -- Morita theory, revisited -- 1. Introduction -- 2. Notations -- 3. Morita theory -- 4. The Lambek theorem -- 5. Self-dual idempotents and Morita algebras -- References -- Universal deformation rings of group representations, with an application of Brauer's generalized decomposition numbers -- 1. Introduction -- 2. Mazur's deformation theory -- 3. Universal deformation rings of modules for finite groups -- 4. Brauer's generalized decomposition numbers and universal deformation rings -- References -- Derived Representation Schemes and Noncommutative Geometry -- 1. Introduction -- Notation and Conventions -- 2. Model categories -- 3. Representation Schemes -- 4. Cyclic Homology and Higher Trace Maps -- 5. Abelianization of the Representation Functor -- 6. Examples -- Acknowledgements -- References -- Classifying torsion pairs for tame hereditary algebras and tubes -- Introduction -- 1. Torsion pairs -- 2. Torsion pairs and tilting for finite dimensional algebras -- 3. Big cotilting modules for finite dimensional algebras -- 4. Tubes -- 5. Combinatorial classifications -- References -- Problems solved by using degrees of irreducible morphisms -- Introduction -- 1. Preliminaries and Notation -- 2. On degrees -- 3. Characterizations of the notion of degree. |
| Record Nr. | UNINA-9910786541503321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Expository lectures on representation theory : Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA / / Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors
| Expository lectures on representation theory : Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA / / Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| Descrizione fisica | 1 online resource (236 p.) |
| Disciplina | 512/.46 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Associative rings
Representations of rings (Algebra) |
| ISBN | 1-4704-1441-4 |
| Classificazione | 16G1016G2016G6016G7020C2016W2514L30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Fine and coarse moduli spaces in the representation theory of finite dimensional algebras -- 1. Introduction and notation -- Acknowledgements -- 2. Affine and projective parametrizations of the Î?-modules of dimension vector -- 3. Quotient varieties on the geometric market"generalities and representation-theoretic particulars -- 4. Rendering Riemann's classification philosophy more concrete -- 5. Approach A: King's adaptation of Mumford stability: Focusing on the objects which are (semi-)stable relative to a weight function -- 6. Approach B. Slicing Î?- into strata with fixed top -- 7. Slicing Î?- more finely, in terms of radical layerings Representation-theoretically optimal coordinatization of ^{ }_{ } -- 8. Problems. Pros and Cons of Approach B -- References -- More Representations of Wild Quivers -- Introduction -- 1. Preliminaries -- 2. Spectral properties of the Coxeter transformations -- 3. Elementary modules -- 4. The regular components -- 5. Partial tilting modules -- 6. The perpendicular category of a rigid regular module -- 7. A functor between categories of regular modules -- 8. Generation of cocones -- 9. Factorisations of morphisms -- References -- Phantom Morphisms and Salce's Lemma -- 1. Introduction -- 2. Preliminaries -- 3. Salce's Lemma -- 4. The Flat Cover Conjecture -- 5. Phantom Morphisms -- 6. Salce's Lemma for Ideals -- 7. Subfunctors of -- 8. Examples -- 9. Quasi-Frobenius Rings -- 10. The Powers of the Phantom Ideal -- References -- Morita theory, revisited -- 1. Introduction -- 2. Notations -- 3. Morita theory -- 4. The Lambek theorem -- 5. Self-dual idempotents and Morita algebras -- References -- Universal deformation rings of group representations, with an application of Brauer's generalized decomposition numbers -- 1. Introduction -- 2. Mazur's deformation theory -- 3. Universal deformation rings of modules for finite groups -- 4. Brauer's generalized decomposition numbers and universal deformation rings -- References -- Derived Representation Schemes and Noncommutative Geometry -- 1. Introduction -- Notation and Conventions -- 2. Model categories -- 3. Representation Schemes -- 4. Cyclic Homology and Higher Trace Maps -- 5. Abelianization of the Representation Functor -- 6. Examples -- Acknowledgements -- References -- Classifying torsion pairs for tame hereditary algebras and tubes -- Introduction -- 1. Torsion pairs -- 2. Torsion pairs and tilting for finite dimensional algebras -- 3. Big cotilting modules for finite dimensional algebras -- 4. Tubes -- 5. Combinatorial classifications -- References -- Problems solved by using degrees of irreducible morphisms -- Introduction -- 1. Preliminaries and Notation -- 2. On degrees -- 3. Characterizations of the notion of degree. |
| Record Nr. | UNINA-9910810326303321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Noncommutative curves of genus zero : related to finite dimensional algebras / / Dirk Kussin
| Noncommutative curves of genus zero : related to finite dimensional algebras / / Dirk Kussin |
| Autore | Kussin Dirk <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina | 516.3/52 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Curves, Algebraic
Representations of rings (Algebra) Noncommutative algebras |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0556-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 0. Background""; ""0.1. Notation""; ""0.2. One-parameter families, generic modules and tameness""; ""0.3. Canonical algebras and exceptional curves""; ""0.4. Tubular shifts""; ""0.5. Tame bimodules and homogeneous exceptional curves""; ""0.6. Rational points""; ""Part 1. The homogeneous case""; ""Chapter 1. Graded factoriality""; ""1.1. Efficient automorphisms""; ""1.2. Prime ideals and universal extensions""; ""1.3. Prime ideals as annihilators""; ""1.4. Noetherianness""; ""1.5. Prime ideals of height one are principal""
""1.6. Unique factorization""""1.7. Examples of graded factorial domains""; ""The non-simple bimodule case""; ""The quaternion case""; ""The square roots case""; ""Chapter 2. Global and local structure of the sheaf category""; ""2.1. Serre's theorem""; ""2.2. Localization at prime ideals""; ""2.3. Noncommutativity and the multiplicities""; ""2.4. Localizing with respect to the powers of a prime element""; ""2.5. Zariski topology and sheafification""; ""Chapter 3. Tubular shifts and prime elements""; ""3.1. Central prime elements""; ""3.2. Non-central prime elements and ghosts"" ""Chapter 4. Commutativity and multiplicity freeness""""4.1. Finiteness over the centre""; ""4.2. Commutativity of the coordinate algebra""; ""4.3. Commutativity of the function field""; ""Chapter 5. Automorphism groups""; ""5.1. The automorphism group of a homogeneous curve""; ""5.2. The structure of Aut(H)""; ""5.3. The twisted polynomial case""; ""5.4. On the Auslander-Reiten translation as functor""; ""5.5. The quaternion case""; ""5.6. The homogeneous curves over the real numbers""; ""5.7. Homogeneous curves with finite automorphism group""; ""Part 2. The weighted case"" ""Chapter 6. Insertion of weights""""6.1. p-cycles""; ""6.2. Insertion of weights into central primes""; ""6.3. Automorphism groups for weighted curves""; ""Chapter 7. Exceptional objects""; ""7.1. Transitivity of the braid group action""; ""7.2. Exceptional objects and graded factoriality""; ""Chapter 8. Tubular exceptional curves""; ""8.1. Slope categories and the rational helix""; ""8.2. The index of a tubular exceptional curve""; ""8.3. A tubular curve of index three""; ""8.4. A related tubular curve of index two""; ""8.5. Line bundles which are not exceptional"" ""Appendix A. Automorphism groups over the real numbers""""A.1. Tables for the domestic and tubular cases""; ""Appendix B. The tubular symbols""; ""Bibliography""; ""Index""; ""A""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U"" |
| Record Nr. | UNINA-9910480625603321 |
|
Kussin Dirk <1967->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Noncommutative curves of genus zero : related to finite dimensional algebras / / Dirk Kussin
| Noncommutative curves of genus zero : related to finite dimensional algebras / / Dirk Kussin |
| Autore | Kussin Dirk <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (146 p.) |
| Disciplina | 516.3/52 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Curves, Algebraic
Representations of rings (Algebra) Noncommutative algebras |
| ISBN | 1-4704-0556-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 0. Background""; ""0.1. Notation""; ""0.2. One-parameter families, generic modules and tameness""; ""0.3. Canonical algebras and exceptional curves""; ""0.4. Tubular shifts""; ""0.5. Tame bimodules and homogeneous exceptional curves""; ""0.6. Rational points""; ""Part 1. The homogeneous case""; ""Chapter 1. Graded factoriality""; ""1.1. Efficient automorphisms""; ""1.2. Prime ideals and universal extensions""; ""1.3. Prime ideals as annihilators""; ""1.4. Noetherianness""; ""1.5. Prime ideals of height one are principal""
""1.6. Unique factorization""""1.7. Examples of graded factorial domains""; ""The non-simple bimodule case""; ""The quaternion case""; ""The square roots case""; ""Chapter 2. Global and local structure of the sheaf category""; ""2.1. Serre's theorem""; ""2.2. Localization at prime ideals""; ""2.3. Noncommutativity and the multiplicities""; ""2.4. Localizing with respect to the powers of a prime element""; ""2.5. Zariski topology and sheafification""; ""Chapter 3. Tubular shifts and prime elements""; ""3.1. Central prime elements""; ""3.2. Non-central prime elements and ghosts"" ""Chapter 4. Commutativity and multiplicity freeness""""4.1. Finiteness over the centre""; ""4.2. Commutativity of the coordinate algebra""; ""4.3. Commutativity of the function field""; ""Chapter 5. Automorphism groups""; ""5.1. The automorphism group of a homogeneous curve""; ""5.2. The structure of Aut(H)""; ""5.3. The twisted polynomial case""; ""5.4. On the Auslander-Reiten translation as functor""; ""5.5. The quaternion case""; ""5.6. The homogeneous curves over the real numbers""; ""5.7. Homogeneous curves with finite automorphism group""; ""Part 2. The weighted case"" ""Chapter 6. Insertion of weights""""6.1. p-cycles""; ""6.2. Insertion of weights into central primes""; ""6.3. Automorphism groups for weighted curves""; ""Chapter 7. Exceptional objects""; ""7.1. Transitivity of the braid group action""; ""7.2. Exceptional objects and graded factoriality""; ""Chapter 8. Tubular exceptional curves""; ""8.1. Slope categories and the rational helix""; ""8.2. The index of a tubular exceptional curve""; ""8.3. A tubular curve of index three""; ""8.4. A related tubular curve of index two""; ""8.5. Line bundles which are not exceptional"" ""Appendix A. Automorphism groups over the real numbers""""A.1. Tables for the domestic and tubular cases""; ""Appendix B. The tubular symbols""; ""Bibliography""; ""Index""; ""A""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U"" |
| Record Nr. | UNINA-9910788855703321 |
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Kussin Dirk <1967->
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| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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