Affine oriented Frobenius Brauer categories

TL;DR

This paper introduces affine oriented Frobenius Brauer categories associated with Frobenius superalgebras and demonstrates their natural actions on supermodule categories of general linear Lie superalgebras with entries in these algebras.

Contribution

It constructs new categorical frameworks for superalgebras and extends existing actions to more general algebraic structures.

Findings

Defined oriented Frobenius Brauer categories for Frobenius superalgebras

Established natural actions on supermodule categories of Lie superalgebras

Generalized previous module actions to broader algebraic contexts

Abstract

To any Frobenius superalgebra $A$ we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer category. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras $\mathfrak{gl}_{m|n}(A)$ with entries in $A$. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where $A$ is the ground field and the two-dimensional Clifford superalgebra, respectively.