The quantum spin Brauer category

Abstract

We introduce a diagrammatic braided monoidal category, the quantum spin Brauer category , together with a full functor to the category of finite-dimensional type- 1 modules for U q ( 𝔰𝔬 ( N ) ) or U q ( 𝔬 ( N ) ) . This functor becomes essentially surjective after passing to the idempotent completion. The quantum spin Brauer category can be thought of as a quantum version of the spin Brauer category introduced in [18]. Alternatively, it is an enlargement of the Kauffman category, obtained by adding a generating object corresponding to the quantum spin module.