Affine Frobenius Brauer Categories

Abstract

We define the affine Frobenius Brauer categories associated to each symmetric involutive Frobenius superalgebra $A$. We then define an action of these categories on the categories of finite-dimensional supermodules for orthosymplectic Lie superalgebras defined over $A$. When $A$ is the base field, we recover the previously-studied affine Brauer category; for other choices of $A$, the categories are novel. Finally, we state a conjecture for bases of homomorphism spaces in affine Frobenius Brauer categories, and outline a potential proof strategy.