English

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 AA. We then define an action of these categories on the categories of finite-dimensional supermodules for orthosymplectic Lie superalgebras defined over AA. When AA is the base field, we recover the previously-studied affine Brauer category; for other choices of AA, 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.

Keywords

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

R2 v1 2026-06-28T15:19:38.490Z