The Heisenberg category of a category

Gyenge, Adam, Koppensteiner, Clemens and Logvinenko, Timothy ORCID: https://orcid.org/0000-0001-5279-6977 2025. The Heisenberg category of a category. Memoirs of the American Mathematical Society

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Abstract

Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical analogue of the Fock space representation of the Heisenberg algebra. Our construction generalises and unifies various categorical Heisenberg algebra actions appearing in the literature. In particular, we give a full categorical enhancement of the action on derived categories of symmetric quotient stacks introduced by Krug, which itself categorifies a Heisenberg algebra action proposed by Grojnowski.

Item Type:	Article
Status:	In Press
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	American Mathematical Society
ISSN:	0065-9266
Date of First Compliant Deposit:	7 October 2025
Date of Acceptance:	22 August 2025
Last Modified:	08 Oct 2025 11:00
URI:	https://orca.cardiff.ac.uk/id/eprint/181535

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