LEADER 04997nam 2200589 450 001 9910810326303321 005 20220902013336.0 010 $a1-4704-1441-4 035 $a(CKB)3710000000124448 035 $a(EBL)3113226 035 $a(SSID)ssj0001235992 035 $a(PQKBManifestationID)11711430 035 $a(PQKBTitleCode)TC0001235992 035 $a(PQKBWorkID)11232370 035 $a(PQKB)11132469 035 $a(MiAaPQ)EBC3113226 035 $a(RPAM)17843003 035 $a(PPN)197102514 035 $a(EXLCZ)993710000000124448 100 $a20140612h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aExpository lectures on representation theory $eMaurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA /$fKiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2014. 210 4$dİ2014 215 $a1 online resource (236 p.) 225 1 $aContemporary mathematics,$x1098-3627 ;$v607$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-9140-5 320 $aIncludes bibliographical references. 327 $aPreface -- 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 I??-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 I??- into strata with fixed top -- 7. Slicing I??- 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. 410 0$aContemporary mathematics (American Mathematical Society).$v607$x0271-4132 606 $aAssociative rings$vCongresses 606 $aRepresentations of rings (Algebra)$vCongresses 615 0$aAssociative rings 615 0$aRepresentations of rings (Algebra) 676 $a512/.46 686 $a16G10$a16G20$a16G60$a16G70$a20C20$a16W25$a14L30$2msc 702 $aIgusa$b Kiyoshi$f1949- 702 $aMartsinkovsky$b A$g(Alex), 702 $aTodorov$b G$g(Gordana), 712 12$aMaurice Auslander Distinguished Lectures and International Conference 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810326303321 996 $aExpository lectures on representation theory$94036007 997 $aUNINA