LEADER 04256nam 22004095a 450 001 9910151928203321 005 20110909234510.0 010 $a3-03719-601-7 024 70$a10.4171/101 035 $a(CKB)3710000000953876 035 $a(CH-001817-3)135-110909 035 $a(PPN)178155977 035 $a(EXLCZ)993710000000953876 100 $a20110909j20110924 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRepresentations of Algebras and Related Topics$b[electronic resource] /$fAndrzej Skowron?ski, Kunio Yamagata 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (740 pages) 225 0 $aEMS Series of Congress Reports (ECR) ;$x2523-515X 327 $tOn generalized cluster categories /$rClaire Amiot --$tModule categories for finite group algebras /$rDavid J. Benson, Srikanth B. Iyengar, Henning Krause --$tOn cluster theory and quantum dilogarithm identities /$rBernhard Keller --$tQuantum loop algebras, quiver varieties, and cluster algebras /$rBernard Leclerc --$tWeighted projective lines and applications /$rHelmut Lenzing --$tCohomology of block algebras of finite groups /$rMarkus Linckelmann --$tAlgebras with separating Auslander-Reiten components /$rPiotr Malicki, Andrzej Skowron?ski --$tClassification problems in noncommutative algebraic geometry and representation theory /$rIzuru Mori --$tPeriodicities in cluster algebras and dilogarithm identities /$rTomoki Nakanishi --$tThe Tits forms of tame algebras and their roots /$rJose? Antonio Pen?a, Andrzej Skowron?ski --$tThe minimal representation-infinite algebras which are special biserial /$rClaus Michael Ringel --$tCoalgebras of tame comodule type, comodule categories, and a tame-wild dichotomy problem /$rDaniel Simson --$tSingularities of orbit closures in module varieties /$rGrzegorz Zwara. 330 $aThis book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, quantum loop algebras, Nakajima quiver varieties, Yang-Baxter equations, T-systems and Y-systems, dilogarithm and quantum dilogarithm identities, stable module categories, localizing and colocalizing subcategories, cohomologies of groups, support varieties, fusion systems, Hochschild cohomologies, weighted projective lines, coherent sheaves, Kleinian and Fuchsian singularities, stable categories of vector bundles, nilpotent operators, Artin-Schelter regular algebras, Fano algebras, deformations of algebras, module varieties, degenerations of modules, singularities of orbit closures, coalgebras and comodules, representation types of algebras and coalgebras, Tits and Euler forms of algebras, Galois coverings of algebras, tilting and cluster tilting theory, algebras of small homological dimensions, Auslander-Reiten theory. The book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of examples and open problems and give new perspectives for research in the field. 606 $aFields & rings$2bicssc 606 $aAssociative rings and algebras$2msc 615 07$aFields & rings 615 07$aAssociative rings and algebras 686 $a16-xx$2msc 702 $aSkowron?ski$b Andrzej 702 $aYamagata$b Kunio 801 0$bch0018173 906 $aBOOK 912 $a9910151928203321 996 $aRepresentations of algebras and related topics$91430594 997 $aUNINA