no. 2
The quantum spin Brauer category
McNamara, Peter J.1 orcid; Savage, Alistair2 orcid 
1School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia
2Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada
Annals of Representation Theory, Volume 3 (2026) no. 2, pp. 247-298

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 in [18]. 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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Accepted:
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DOI: 10.5802/art.41
Classification: 18M15, 18M30, 17B37
Keywords: Quantum group, quantized enveloping algebra, special orthogonal Lie algebra, spin group, orthogonal group, monoidal category, string diagram, graphical calculus, Deligne category, interpolating category

McNamara, Peter J.  1 ; Savage, Alistair  2

1 School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia
2 Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
McNamara, Peter J.; Savage, Alistair. The quantum spin Brauer category. Annals of Representation Theory, Volume 3 (2026) no. 2, pp. 247-298. doi: 10.5802/art.41
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