On periodicity in bounded projective resolutions

Details On periodicity in bounded projective resolutions On periodicity in bounded projective resolutions

2012-03-12

arxiv.org/abs/1203.2408v1

Mathematics

Representation Theory

Scientific paper

Let A be a self-injective algebra over an algebraically closed field k. We show that if an A-module M of complexity one has an open orbit in the variety of d-dimensional A-modules, then M is periodic. As a corollary we see that any simple A-module of complexity one must be periodic. In the course of the proof, we also show that modules with open orbits are preserved by stable equivalences of Morita type between self-injective algebras.

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