Constructing new braided \(T\)-categories over weak Hopf algebras.
Let \(H\) be a Hopf algebra with bijective antipode, and consider two Hopf algebra automorphisms \(\alpha\) and \(\beta\) of \(H\). \textit{F.~Panaite} and \textit{M.~D.~Staic} [Isr. J. Math. 158, 349-365 (2007; Zbl 1128.16026)] have introduced a twisted notion of Yetter-Drinfeld modules, termed \((\alpha,\beta)\)-Yetter-Drinfeld modules. The disjoint union of the categories of \((\alpha,\beta)\)-Yetter-Drinfeld modules is a braided crossed group category in the sense of Turaev; if \(H\) is finite dimensional, then this category is a representation category over a suitable version of the Drinfeld double. In the present paper, these results are generalized to the situation where \(H\) is a weak Hopf algebra with bijective antipode.
scientific article; zbMATH DE number 5774833
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