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2007-07

Stable Calabi-Yau dimension for finite type selfinjective algebras

by Holm, Thorsten, Jorgensen, Peter.


Series: 2007-07, Preprints

MSC:
16G70 ~Auslander-Reiten sequences (almost split sequences) and ~Auslander-Reiten quivers
18E30 Derived categories, triangulated categories
16D50 Injective modules, self-injective rings
16G10 Representations of Artinian rings
16G60 Representation type (finite, tame, wild, etc.)

Abstract:
We show that the Calabi-Yau dimension of the stable
module category of a selfinjective algebra of finite
representation type is determined by the action of
the Nakayama and suspension functors on objects.
Our arguments are based on recent results of C. Amiot,
and hence apply more generally to triangulated
categories having only finitely many indecomposable
objects.

Keywords:
Calabi-Yau dimensions, Triangulated categories, Stable module categories, Selfinjective algebras, Auslander-Reiten quivers