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arXiv · 2006.09626

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

Mengmeng Gao·Hebing Rui·Linliang Song
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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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Mengmeng Gao, Hebing Rui, Linliang Song. 2020-06-17. A basis theorem for the affine Kauffmann category and its cyclotomic quotients. https://arxiv.org/abs/2006.09626

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