Serre functors and graded categories

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Grant, Joseph (2023) Serre functors and graded categories. Algebras and Representation Theory, 26 (5). 2113–2180. ISSN 1386-923X

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Abstract

We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k-linear categories: categories with group actions and categories with graded hom spaces. We check that Serre structures are preserved by taking orbit categories and skew group categories, and describe the relationship with graded Frobenius algebras. Using a formal version of Auslander-Reiten translations, we show that the derived category of a d-representation finite algebra is fractionally Calabi-Yau if and only if its preprojective algebra has a graded Nakayama automorphism of finite order. This connects various results in the literature and gives new examples of fractional Calabi-Yau algebras.

Item Type:	Article
Uncontrolled Keywords:	derived picard group,enriched category,fractional calabi-yau,orbit category,preprojective algebra,serre functor,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
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)
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/2007.01817
Depositing User:	LivePure Connector
Date Deposited:	12 Jul 2022 09:31
Last Modified:	03 Jun 2025 23:53
URI:	https://ueaeprints.uea.ac.uk/id/eprint/86072
DOI:	10.1007/s10468-022-10151-4

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