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

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2014; ©2014
• Descrizione fisica: 1 online resource (236 p.)
• Disciplina: 512/.46
• Soggetto topico: Associative rings; Representations of rings (Algebra)
• Classificazione: 16G1016G2016G6016G7020C2016W2514L30
• Persona (resp. second.): IgusaKiyoshi <1949->; MartsinkovskyA (Alex); TodorovG (Gordana)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• 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.
• Titolo autorizzato: Expository lectures on representation theory
• ISBN: 1-4704-1441-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910810326303321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society). ; 607 . 0271-4132