Affine Frobenius Brauer Categories
Representation Theory
2025-09-22 v2 Category Theory
Abstract
We define the affine Frobenius Brauer categories associated to each symmetric involutive Frobenius superalgebra . We then define an action of these categories on the categories of finite-dimensional supermodules for orthosymplectic Lie superalgebras defined over . When is the base field, we recover the previously-studied affine Brauer category; for other choices of , 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.
Cite
@article{arxiv.2403.09103,
title = {Affine Frobenius Brauer Categories},
author = {Saima Samchuck-Schnarch},
journal= {arXiv preprint arXiv:2403.09103},
year = {2025}
}
Comments
23 pages; v2: published version with tweaks and improvements throughout, and an expanded and corrected version of Section 4