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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 | ||
| ||