Frobenius Brauer Categories

Given a symmetric Frobenius superalgebra A equipped with a compatible involution, we define the associated Frobenius Brauer category B(A) and affine Frobenius Brauer category AB(A), generalizing the plain Brauer category B and affine Brauer category AB. We define the orthosymplectic Lie superalgebra osp m|2n(A) and a functor from B(A) to osp m|2n(A)-mod, the category of supermodules over osp m|2n(A). We also define a functor from AB(A) to the endofunctor supercategory of osp m|2n(A)-mod.We prove that these two functors are well-defined and use the former functor to prove a basis result for B(A, δ), a specialized version of B(A). Prior to defining these categories and functors, we provide the background information on super-mathematics and Frobenius superalgebras needed to understand the new results.

Grantor dc:publisher

Université d'Ottawa / University of Ottawa

Year dc:date

2022

Author dc:creator

• Samchuck-Schnarch, Saima

Contributors dc:contributor

• Savage, Alistair

• pure mathematics
• string diagrams
• category theory
• representation theory

Language dc:language

en

Identifier

http://dx.doi.org/10.20381/ruor-28137

OAI identifier oai:identifier

oai:ruor.uottawa.ca:10393/43924