The Heisenberg category of a category
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911226755284992 |
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| author | Gyenge, Ádám Koppensteiner, Clemens Logvinenko, Timothy |
| author_facet | Gyenge, Ádám Koppensteiner, Clemens Logvinenko, Timothy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_13334 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Heisenberg category of a category Gyenge, Ádám Koppensteiner, Clemens Logvinenko, Timothy Algebraic Geometry Category Theory Representation Theory 18N25 (primary), 14F08 (secondary) 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. |
| title | The Heisenberg category of a category |
| topic | Algebraic Geometry Category Theory Representation Theory 18N25 (primary), 14F08 (secondary) |
| url | https://arxiv.org/abs/2105.13334 |