The quantum spin Brauer category
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916703698419712 |
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| author | McNamara, Peter J. Savage, Alistair |
| author_facet | McNamara, Peter J. Savage, Alistair |
| contents | We introduce a diagrammatic braided monoidal category, the quantum spin Brauer category, together with a full functor to the category of finite-dimensional, type $1$ modules for $U_q(\mathfrak{so}(N))$ or $U_q(\mathfrak{o}(N))$. This functor becomes essentially surjective after passing to the idempotent completion. The quantum spin Brauer category can be thought of as a quantum version of the spin Brauer category introduced previously by the authors. Alternatively, it is an enlargement of the Kauffman category, obtained by adding a generating object corresponding to the quantum spin module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantum spin Brauer category McNamara, Peter J. Savage, Alistair Quantum Algebra Representation Theory 18M15, 18M30, 17B37 We introduce a diagrammatic braided monoidal category, the quantum spin Brauer category, together with a full functor to the category of finite-dimensional, type $1$ modules for $U_q(\mathfrak{so}(N))$ or $U_q(\mathfrak{o}(N))$. This functor becomes essentially surjective after passing to the idempotent completion. The quantum spin Brauer category can be thought of as a quantum version of the spin Brauer category introduced previously by the authors. Alternatively, it is an enlargement of the Kauffman category, obtained by adding a generating object corresponding to the quantum spin module. |
| title | The quantum spin Brauer category |
| topic | Quantum Algebra Representation Theory 18M15, 18M30, 17B37 |
| url | https://arxiv.org/abs/2504.16618 |