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Twisted Bimodules and Hochschild Cohomology for Self-Injective Algebras of Class A_n

by Erdmann, K., Holm, T..

Series: 1997-13, Preprints

16D20 Bimodules
16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
16G60 Representation type (finite, tame, wild, etc.)
16G70 ~Auslander-Reiten sequences (almost split sequences) and ~Auslander-Reiten quivers

We study stable homomorphisms for twisted bimodule structures
on a finite-dimensional self-injective algebra. We use this to give
a presentation for the Hochschild cohomology ring of self-injective
Nakayama algebras. By derived equivalence, this gives also the Hochschild
cohomology ring for arbitrary self-injective algebras whose stable Auslander-
Reiten quiver is of the form (Z)A n = ! 8 e ?. Moreover, we obtain a
new characterization of self-injective Nakayama algebras.


This paper was published in:
Forum Mathematicum 11 (1999), 177-201