Simple-minded systems, configurations and mutations for representation-finite self-injective algebras. (English) Zbl 1358.16012
Summary: 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.
MSC:
| 16G10 | Representations of associative Artinian rings |
| 16D50 | Injective modules, self-injective associative rings |
| 16D90 | Module categories in associative algebras |
| 16E35 | Derived categories and associative algebras |
Keywords:
self-injective algebra; simple-minded systems; Nakayama-stable simple-minded collections; mutationsReferences:
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