Simple-minded systems, configurations and mutations for representation-finite self-injective algebras

2013/05/12 by Aaron Chan, Chan, Aaron, Steffen Koenig +3
Mathematics · #13D09 #16G10 #18Axx #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:13D09 #msc:16G10 #msc:18Axx

paper · pdf · doi:10.48550/arxiv.1305.2576

25pages

arxiv created 2013/05/12 · arxiv updated 2013/05/14

Abstract

Simple-minded systems of objects in a stable module category are defined by common properties with the set of simple modules, whose images under stable equivalences do form simple-minded systems. Over a representation-finite self-injective algebra, it is shown that all simple-minded systems are images of simple modules under stable equivalences of Morita type, and that all simple-minded systems can be lifted to Nakayama-stable simple-minded collections in the derived category. In particular, all simple-minded systems can be obtained algorithmically using mutations.

Related

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