The N-stable category

Brightbill, Jeremy R. B. and Miemietz, Vanessa (2024) The N-stable category. Mathematische Zeitschrift, 307 (4). ISSN 0025-5874

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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 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.

Item Type:	Article
Additional Information:	Funding information: V.M. is partially supported by EPSRC grant EP/S017216/1. Part of this research was carried out during a research visit of J.B. to the University of East Anglia, whose hospitality is gratefully acknowledged.
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	14 May 2024 08:14
Last Modified:	22 Jul 2024 10:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/95136
DOI:	10.1007/s00209-024-03518-4

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