论文标题
Affine Kauffmann类别及其环形词的基础定理
A basis theorem for the affine Kauffmann category and its cyclotomic quotients
论文作者
论文摘要
Aggine Kauffmann类别是严格的单体类别，可以被视为Affine Brauer类别的$ Q $ - Analogue（Rui等人的数学Zeit。293，503-550，2019）。在本文中，我们证明了Aggine Kauffmann类别中形态空间的基础定理。 Cyclotomic Kauffmann类别是Aggine Kauffmann类别的商类别。我们还证明，如果且仅当$ \ Mathbf u $ $ $加热条件在定义意义上，则此类别中的任何形态空间都是自由的，并且仅当$ \ mathbf u $ $ $ $ $ $ $ $ $ $ $ $ $ \ mathbb k $具有最大排名。
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.
