Periodic resolutions and self-injective algebras of finite type

Details Periodic resolutions and self-injective algebras of finite type Periodic resolutions and self-injective algebras of finite type

2008-08-09

arxiv.org/abs/0808.1311v2

Mathematics

Representation Theory

New version includes proof of periodicity for nonstandard algebras. Presentation of Sections 2 and 3 is modified to treat more

Scientific paper

We say that an algebra A is periodic if it has a periodic projective resolution as an (A,A)-bimodule. We show that any self-injective algebra of finite representation type is periodic. To prove this, we first apply the theory of smash products to show that for a finite Galois covering B --> A, B is periodic if and only if A is. In addition, when A has finite representation type, we build upon results of Buchweitz to show that periodicity passes between A and its stable Auslander algebra. Finally, we use Asashiba's classification of the derived equivalence classes of self-injective algebras of finite type to compute bounds for the periods of these algebras, and give an application to stable Calabi-Yau dimensions.

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