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- W4310421355 abstract "For a semisimple quasi-triangular Hopf algebra $left( H,Rright) $ over a field $k$ of characteristic zero, and a strongly separable quantum commutative $H$-module algebra $A$ over which the Drinfeld element of $H$ acts trivially, we show that $A#H$ is a weak Hopf algebra, and it can be embedded into a weak Hopf algebra $operatorname{End}A^{ast}otimes H$. With these structure, $_{A#H}operatorname{Mod}$ is the monoidal category introduced by Cohen and Westreich, and $_{operatorname{End}A^{ast}otimes H}mathcal{M}$ is tensor equivalent to $_{H}mathcal{M}$. If $A$ is in the M{{u}}ger center of $_{H}{mathcal{M}}$, then the embedding is a quasi-triangular weak Hopf algebra morphism. This explains the presence of a subgroup inclusion in the characterization of irreducible Yetter-Drinfeld modules for a finite group algebra." @default.
- W4310421355 created "2022-12-10" @default.
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- W4310421355 date "2022-11-28" @default.
- W4310421355 modified "2023-10-16" @default.
- W4310421355 title "Weak Hopf Algebras, Smash Products and Applications to Adjoint-Stable Algebras" @default.
- W4310421355 doi "https://doi.org/10.48550/arxiv.2211.15191" @default.
- W4310421355 hasPublicationYear "2022" @default.
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