Author:
Brightbill Jeremy R. B.,Miemietz Vanessa
Abstract
AbstractA 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 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 Grothendieck abelian category. We also compute the Serre functor on the N-stable category over a self-injective algebra and study the resultant fractional Calabi–Yau properties.
Publisher
Springer Science and Business Media LLC
Reference29 articles.
1. Bahiraei, P., Hafezi, R., Nematbakhsh, A.: Homotopy category of $$N$$-complexes of projective modules. J. Pure Appl. Algebra 220(6), 2414–2433 (2016)
2. Beligiannis, A., Reiten, I.: Homological and Homotopical Aspects of Torsion Theories. American Mathematical Society, Providence (2007)
3. Borceux, F.: Handbook of Categorical Algebra: vol. 1, Basic Category Theory, vol. 1. Cambridge University Press, Cambridge (1994)
4. Buchweitz, R.-O.: Maximal Cohen–Macaulay modules and Tate-cohomology over Gorenstein rings (1987)
5. Bühler, T.: Exact categories. Expositiones Mathematicae 28(1), 1–69 (2010)