The $N$-Stable Category
Representation Theory
2021-11-16 v2 Category Theory
Abstract
A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy category of acyclic complexes of projectives, and the singularity category. To adapt this result to -complexes, one must find an appropriate candidate for the -analogue of the stable category. We identify this "-stable category" via the monomorphism category and prove Buchweitz's theorem for -complexes over a Frobenius exact abelian category. We also compute the Serre functor on the -stable category over a self-injective algebra and study the resultant fractional Calabi-Yau properties.
Cite
@article{arxiv.2109.07728,
title = {The $N$-Stable Category},
author = {Jeremy R. B. Brightbill and Vanessa Miemietz},
journal= {arXiv preprint arXiv:2109.07728},
year = {2021}
}
Comments
51 pages. References added to introduction, results in Section 3 strengthened