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ToolsBrightbill, 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 |
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| 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 (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR) |
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| Depositing User: | LivePure Connector |
| Date Deposited: | 14 May 2024 08:14 |
| Last Modified: | 10 Dec 2024 01:44 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/95136 |
| DOI: | 10.1007/s00209-024-03518-4 |
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