Affine Frobenius Brauer Categories
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915501486112768 |
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| author | Samchuck-Schnarch, Saima |
| author_facet | Samchuck-Schnarch, Saima |
| contents | We define the affine Frobenius Brauer categories associated to each symmetric involutive Frobenius superalgebra $A$. We then define an action of these categories on the categories of finite-dimensional supermodules for orthosymplectic Lie superalgebras defined over $A$. When $A$ is the base field, we recover the previously-studied affine Brauer category; for other choices of $A$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine Frobenius Brauer Categories Samchuck-Schnarch, Saima Representation Theory Category Theory 18M30, 18M05, 17B10 We define the affine Frobenius Brauer categories associated to each symmetric involutive Frobenius superalgebra $A$. We then define an action of these categories on the categories of finite-dimensional supermodules for orthosymplectic Lie superalgebras defined over $A$. When $A$ is the base field, we recover the previously-studied affine Brauer category; for other choices of $A$, 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. |
| title | Affine Frobenius Brauer Categories |
| topic | Representation Theory Category Theory 18M30, 18M05, 17B10 |
| url | https://arxiv.org/abs/2403.09103 |