2012/03/12 by Alex Dugas, Dugas, Alex
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1203.2408
arxiv created 2012/03/12 · openalex publication_date 2012/03/12 · arxiv updated 2012/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.