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

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.

57 pages

References in corpus (2)

• The Cyclotomic Birman-Murakami-Wenzl Algebras
• Representations of the oriented skein category

Cited by in corpus (1)

• Representations of weakly triangular categories