Trends in Representation Theory of Algebras and Related Topics: Workshop on Representations of Algebras and Related Topics, August 11-14, 2004, Querétaro, MéxicoJosé Antonio de la Peña, Raymundo Bautista This book is based on lectures given during a Workshop on Representations of Algebras and Related Topics. Some additional articles are included in order to complete a panoramic view of the main trends of the subject. The volume contains original presentations by leading algebraists addressed to specialists as well as to a broader mathematical audience. The articles include new proofs, examples, and detailed arguments. Topics under discussion include moduli spaces associated to quivers, canonical basis of quantum algebras, categorifications and derived categories, $A$-infinity algebras and functor categories, cluster algebras, support varieties for modules and complexes, the Gabriel-Roiter measure for modules, and selfinjective algebras. |
Contents
| 1 | |
Introduction to moduli spaces associated to quivers | 31 |
A theorem of Peng and Xiao | 51 |
Ainfinity algebras modules and functor categories | 67 |
Rouquiers theorem on representation dimension | 95 |
Foundation of the representation theory of Artin algebras using the GabrielRoiter measure | 105 |
Categorification of sl2 and braid groups | 137 |
Finite and tame type | 169 |
Support varieties for modules and complexes | 239 |
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Common terms and phrases
A-modules Aeo-algebra alge algebras of Euclidean algebras of finite algebras of polynomial artin algebra augmented k-quivers Auslander-Reiten quiver automorphism categorification cluster algebras cluster category cluster-tilted algebra cohomology ring commutative complex corresponding defined denote derived category derived equivalent dimension direct sum dual canonical basis Dynkin type elements Euclidean type example Fg1 and Fg2 finite dimensional algebra finite type finitely generated module functor Gabriel-Roiter measure given graded group rings hereditary algebra Hochschild cohomology Hochschild cohomology ring homotopy Hopf algebras indecomposable modules indecomposable submodules infinite injective isomorphism classes k-algebra Koszul algebras Lemma Math module category moduli spaces monomorphism morphism Noetherian polynomial growth Preprint proof Proposition quasi-isomorphism quotient representation theory representation type satisfy Fg1 selfinjective algebras simple modules Skowroński socle stable equivalence subalgebra subcategory support varieties symmetric algebras THEOREM tilted algebra tilting object triangulated category trivial extension tubular type vector VH(M Zelevinsky