Odd Khovanov homology and higher representation theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909126440779776 |
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| author | Schelstraete, Léo Vaz, Pedro |
| author_facet | Schelstraete, Léo Vaz, Pedro |
| contents | We define a supercategorification of the $q$-Schur algebra of level two and an odd analogue of $\mathfrak{gl}_2$-foams. Using these constructions, we define a homological invariant of tangles, and show that it coincides with odd Khovanov homology when restricted to links. This gives a representation theoretic construction of odd Khovanov homology. In the process, we define a tensor product on the category of chain complexes in super-2-categories which is compatible with homotopies. This could be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14394 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Odd Khovanov homology and higher representation theory Schelstraete, Léo Vaz, Pedro Geometric Topology Quantum Algebra Representation Theory We define a supercategorification of the $q$-Schur algebra of level two and an odd analogue of $\mathfrak{gl}_2$-foams. Using these constructions, we define a homological invariant of tangles, and show that it coincides with odd Khovanov homology when restricted to links. This gives a representation theoretic construction of odd Khovanov homology. In the process, we define a tensor product on the category of chain complexes in super-2-categories which is compatible with homotopies. This could be of independent interest. |
| title | Odd Khovanov homology and higher representation theory |
| topic | Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2311.14394 |