Affine oriented Frobenius Brauer categories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866908360857616384 |
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| author | McSween, Alexandra Savage, Alistair |
| author_facet | McSween, Alexandra Savage, Alistair |
| contents | To any Frobenius superalgebra $A$ we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer category. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras $\mathfrak{gl}_{m|n}(A)$ with entries in $A$. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where $A$ is the ground field and the two-dimensional Clifford superalgebra, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_04582 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Affine oriented Frobenius Brauer categories McSween, Alexandra Savage, Alistair Representation Theory Category Theory 18M05, 18M30, 17B10 To any Frobenius superalgebra $A$ we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer category. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras $\mathfrak{gl}_{m|n}(A)$ with entries in $A$. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where $A$ is the ground field and the two-dimensional Clifford superalgebra, respectively. |
| title | Affine oriented Frobenius Brauer categories |
| topic | Representation Theory Category Theory 18M05, 18M30, 17B10 |
| url | https://arxiv.org/abs/2101.04582 |