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A basis theorem for the affine Kauffmann category and its cyclotomic quotients

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arxiv 2006.09626 v1 pith:IASCTRDW submitted 2020-06-17 math.RT math.QA

Mengmeng Gao , Hebing Rui , Linliang Song This is my paper · ORCID
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keywords categoryaffinekauffmannbasiscyclotomicmorphismprovetheorem
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abstract

The affine Kauffmann category is a strict monoidal category and can be considered as a $q$-analogue of the affine Brauer category in (Rui et al. in Math. Zeit. 293, 503-550, 2019). In this paper, we prove a basis theorem for the morphism spaces in the affine Kauffmann category. The cyclotomic Kauffmann category is a quotient category of the affine Kauffmann category. We also prove that any morphism space in this category is free over an integral domain $\mathbb K$ with maximal rank if and only if the $\mathbf u$-admissible condition holds in the sense of Definition 1.13.

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  1. The quantum spin Brauer category

    math.QA 2025-04 accept novelty 7.0 of 10

    The quantum spin Brauer category is a braided diagrammatic category whose Karoubi completion covers all finite-dimensional U_q(so(N)) and U_q(o(N)) modules, including spin modules.

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