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arXiv · 2504.16618

The quantum spin Brauer category

Peter J. McNamara·Alistair Savage
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Abstract

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.

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Peter J. McNamara, Alistair Savage. 2025-04-23. The quantum spin Brauer category. https://arxiv.org/abs/2504.16618

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