Defines higher-level affine wreath product algebras and higher-level affine Frobenius Hecke algebras as path algebras of categories depending on a Frobenius superalgebra, yielding new analogues of degenerate affine Hecke and affine Sergeev algebras.
Monoidal supercategories
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abstract
In the literature, one finds several competing notions for the super (i.e., Z/2-graded) analog of a monoidal category. The goal of this paper is to clarify these definitions and the connections between them. We also discuss in detail the example of the odd Temperley-Lieb supercategory. In a forthcoming article, we will exploit the formalism developed here in order to define super analogs of the Kac-Moody 2-categories of Khovanov-Lauda and Rouquier.
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Higher-level affine wreath product algebras
Defines higher-level affine wreath product algebras and higher-level affine Frobenius Hecke algebras as path algebras of categories depending on a Frobenius superalgebra, yielding new analogues of degenerate affine Hecke and affine Sergeev algebras.