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.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/43924 |
| Date | 16 August 2022 |
| Creators | Samchuck-Schnarch, Saima |
| Contributors | Savage, Alistair |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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