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 K with maximal rank if and only if the u-admissible condition holds in the sense of Definition 1.13.

Representations of cyclotomic oriented Brauer categories

“…Clearly, it is easy to see that any category which admits an upper finite triangular decomposition is an upper finite weakly triangular category. Moreover, cyclotomic oriented Brauer categories, cyclotomic Brauer categories [20] and cyclotomic Kauffman categories [10] are upper finite weakly triangular categories [11], but it is not clear whether these categories admit triangular decompositions. It is proved in [11] that C-lfdmod is an upper finite fully stratified category if C is the locally unital algebra associated to an upper finite weakly triangular category.…”