Monoidal categorification of genus zero skein algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908370699550720 |
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| author | Allegretti, Dylan G. L. Kim, Hyun Kyu Shan, Peng |
| author_facet | Allegretti, Dylan G. L. Kim, Hyun Kyu Shan, Peng |
| contents | We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monoidal categorification of genus zero skein algebras Allegretti, Dylan G. L. Kim, Hyun Kyu Shan, Peng Representation Theory High Energy Physics - Theory Geometric Topology Quantum Algebra We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston. |
| title | Monoidal categorification of genus zero skein algebras |
| topic | Representation Theory High Energy Physics - Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2505.13332 |