The $N$Stable Category
Abstract
A wellknown 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 $N$complexes, one must find an appropriate candidate for the $N$analogue of the stable category. We identify this "$N$stable category" via the monomorphism category and prove Buchweitz's theorem for $N$complexes over a Frobenius exact abelian category. We also compute the Serre functor on the $N$stable category over a selfinjective algebra and study the resultant fractional CalabiYau properties.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.07728
 Bibcode:
 2021arXiv210907728B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Category Theory;
 16E35
 EPrint:
 51 pages. References added to introduction, results in Section 3 strengthened