Socle deformations of selfinjective algebras of tubular type. (English) Zbl 1137.16024

Białkowski, Jerzy; Skowroński, Andrzej

J. Math. Soc. Japan 56, No. 3, 687-716 (2004).

Summary: We classify all selfinjective finite dimensional algebras over an algebraically closed field which are socle equivalent to the tame selfinjective algebras which admit simply connected Galois coverings and whose Auslander-Reiten quiver consists only of stable tubes.

MSC:

16G60	Representation type (finite, tame, wild, etc.) of associative algebras
16D50	Injective modules, self-injective associative rings
16G70	Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G30	Representations of orders, lattices, algebras over commutative rings

Keywords:

repetitive algebras; tubular algebras; socle equivalences; tame selfinjective algebras; simply connected Galois coverings; Auslander-Reiten quivers; stable tubes