Gyenge, Adam, Koppensteiner, Clemens and Logvinenko, Timothy  ORCID: https://orcid.org/0000-0001-5279-6977
2026.
The Heisenberg category of a category.
Memoirs of the American Mathematical Society
320
, 1633.
10.1090/memo/1633
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Official URL: https://doi.org/10.1090/memo/1633
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 |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| 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: | 20 Oct 2026 09:45 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/181535 |
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