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

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.

25pages

References in corpus (3)

• Tilting mutation of weakly symmetric algebras and stable equivalence
• On tilting complexes providing derived equivalences that send simple-minded objects to simple objects
• Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras

Cited by in corpus (1)

• Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras