Two questions on stable equivalences of Morita type
It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.
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arXiv subjects
Yuming Liu
Publications and source records attributed to Yuming Liu.
Simple-minded systems, configurations and mutations for representation-finite self-injective algebras
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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Simple-minded systems in stable module categories
Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant under stable equivalences; thus the set of all simple-minded systems is an invariant of a stable module category. The simple-minded systems of several classes of algebras are described and connections to the Auslander-Reiten conjecture are pointed out.
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