Frobenius Brauer Categories

Abstract

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.