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- W2477357274 abstract "We construct two functors from the submodule category of a self-injective representation-finite algebra $Lambda$ to the module category of the stable Auslander algebra of $Lambda$. These functors factor through the module category of the Auslander algebra of $Lambda$. Moreover they induce equivalences from the quotient categories of the submodule category modulo their respective kernels and said kernels have finitely many indecomposable objects up to isomorphism. Their construction uses a recollement of the module category of the Auslander algebra induced by an idempotent and this recollement determines a characteristic tilting and cotilting module. If $Lambda$ is taken to be a Nakayama algebra, then said tilting and cotilting module is a characteristic tilting module of a quasi-hereditary structure on the Auslander algebra. We prove that the self-injective Nakayama algebras are the only algebras with this property." @default.
- W2477357274 created "2016-08-23" @default.
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- W2477357274 date "2017-09-01" @default.
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- W2477357274 title "From submodule categories to the stable Auslander algebra" @default.
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- W2477357274 doi "https://doi.org/10.1016/j.jalgebra.2017.05.012" @default.
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