A basis theorem for the affine oriented Brauer category and its cyclotomic quotients

TL;DR

This paper establishes a basis theorem for the morphism spaces in the affine oriented Brauer category and its cyclotomic quotients, providing a foundational understanding of their algebraic structure.

Contribution

It introduces a basis theorem for the affine oriented Brauer category and its cyclotomic quotients, advancing the algebraic understanding of these categories.

Findings

Proved a basis theorem for morphism spaces

Established basis for cyclotomic quotients

Enhanced understanding of affine oriented Brauer categories

Abstract

The affine oriented Brauer category is a monoidal category obtained from the oriented Brauer category (= the free symmetric monoidal category generated by a single object and its dual) by adjoining a polynomial generator subject to appropriate relations. In this article, we prove a basis theorem for the morphism spaces in this category, as well as for all of its cyclotomic quotients.