04233nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084001500185245011300200260008200313300003400395336002600429337002600455338003600481347002400517490005400541505112400595506006601719520185601785650002703641650004003668700003503708700003003743856003203773856006603805135-110909CH-001817-320110909234510.0a fot ||| 0|cr nn mmmmamaa110909e20110924sz fot ||| 0|eng d a978303719601470a10.4171/1012doi ach0018173 7aPBFL2bicssc a16-xx2msc10aRepresentations of Algebras and Related Topicsh[electronic resource] /cAndrzej Skowroński, Kunio Yamagata3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2011 a1 online resource (740 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tOn 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 Skowroński --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 /rJosé Antonio Peña, Andrzej Skowroński --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.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aFields & rings2bicssc07aAssociative rings and algebras2msc1 aSkowroński, Andrzej,eeditor.1 aYamagata, Kunio,eeditor.40uhttps://doi.org/10.4171/101423cover imageuhttps://www.ems-ph.org/img/books/icra14_mini.jpg