REALIZING HIGHER CLUSTER CATEGORIES OF DYNKIN TYPE AS STABLE MODULE CATEGORIES
Copyright policy )REALIZING HIGHER CLUSTER CATEGORIES OF DYNKIN TYPE AS STABLE MODULE CATEGORIES
We show that the stable module categories of certain selfinjective algebras of finite representation type having tree class A_n, D_n, E_6, E_7 or E_8 are triangulated equivalent to u-cluster categories of the corresponding Dynkin type. The proof relies on the 'Morita' theorem for u-cluster categories by Keller and Reiten, along with the recent computation of Calabi-Yau dimensions of stable module categories by Dugas.
26 pages. This paper supersedes withdrawn preprints math.RT/0610728 and math.RT/0612451 which based the computation of Calabi-Yau dimensions on an erroneous result. The problem is circumvented here by using a recent paper of Alex Dugas
- Newcastle University United Kingdom
- University of Hannover Germany
cluster algebras, Cluster algebras, Derived categories and associative algebras, Primary: 16D50, 18E30, Secondary: 05E99, 13F60, 16G10, 16G60, 16G70, Derived categories, triangulated categories, stable module categories, self-injective algebras of finite representation type, Module categories in associative algebras, FOS: Mathematics, Representations of quivers and partially ordered sets, Representation Theory (math.RT), Mathematics - Representation Theory, Representations of associative Artinian rings, cluster categories
cluster algebras, Cluster algebras, Derived categories and associative algebras, Primary: 16D50, 18E30, Secondary: 05E99, 13F60, 16G10, 16G60, 16G70, Derived categories, triangulated categories, stable module categories, self-injective algebras of finite representation type, Module categories in associative algebras, FOS: Mathematics, Representations of quivers and partially ordered sets, Representation Theory (math.RT), Mathematics - Representation Theory, Representations of associative Artinian rings, cluster categories
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