Periodic resolutions and self-injective algebras of finite type
Abstract
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.
Keywords
Cite
@article{arxiv.0808.1311,
title = {Periodic resolutions and self-injective algebras of finite type},
author = {Alex Dugas},
journal= {arXiv preprint arXiv:0808.1311},
year = {2016}
}
Comments
New version includes proof of periodicity for nonstandard algebras. Presentation of Sections 2 and 3 is modified to treat more general gradings. Other minor changes throughout