Affine oriented Frobenius Brauer categories. (English) Zbl 1506.18020
Summary: 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.
MSC:
| 18M05 | Monoidal categories, symmetric monoidal categories |
| 18M30 | String diagrams and graphical calculi |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
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