A semisimple subcategory of Khovanov's Heisenberg category
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912767547539456 |
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| author | Miller, Sam K. |
| author_facet | Miller, Sam K. |
| contents | We show the existence of a semisimple replete subcategory of Khovanov's Heisenberg category that retains the isomorphism data of objects for the full category. This leads to a noncommutative tensor-triangular geometric example of a monoidal triangulated category whose Balmer spectrum satisfies the tensor product property but which contains one-sided thick tensor-ideals that are not two-sided, and whose standard support varieties fail to classify one-sided thick tensor-ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A semisimple subcategory of Khovanov's Heisenberg category Miller, Sam K. Representation Theory Category Theory 18M05, 18M30, 18G80, 18F70 We show the existence of a semisimple replete subcategory of Khovanov's Heisenberg category that retains the isomorphism data of objects for the full category. This leads to a noncommutative tensor-triangular geometric example of a monoidal triangulated category whose Balmer spectrum satisfies the tensor product property but which contains one-sided thick tensor-ideals that are not two-sided, and whose standard support varieties fail to classify one-sided thick tensor-ideals. |
| title | A semisimple subcategory of Khovanov's Heisenberg category |
| topic | Representation Theory Category Theory 18M05, 18M30, 18G80, 18F70 |
| url | https://arxiv.org/abs/2512.13968 |