Diagram categories of Brauer type

TL;DR

This paper develops monoidal (super)categories similar to the Brauer category, constructing bases of hom-spaces with diagrams, and classifies their deformations, including new exotic categories.

Contribution

It introduces new categories of Brauer type, constructs bases for their hom-spaces, and classifies their deformations within a unified framework.

Findings

BWM-category is the unique deformation of the Brauer category.

Periplectic Brauer category has two distinct deformations.

Constructed bases of hom-spaces using Brauer diagrams.

Abstract

This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categories include the Brauer category, its deformation the BWM-category, the periplectic Brauer category, and its deformation the periplectic $q$-Brauer category but also some new exotic categories. We show that the BWM-category is the unique deformation of the Brauer category in this framework, while the periplectic Brauer category has two deformations, which are each other monoidal opposite.