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arXiv · 1305.2576

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

Aaron Chan·Steffen Koenig·Yuming Liu
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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.

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Aaron Chan, Steffen Koenig, Yuming Liu. 2013-05-12. Simple-minded systems, configurations and mutations for representation-finite self-injective algebras. https://arxiv.org/abs/1305.2576

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