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)
• Soggetto genere / forma: Electronic books.
• 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 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""
• 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.: 9910479985603321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society) ; ; Volume 607.