Quantum Double for QuasiHopf Algebras

Abstract

We introduce a quantum double quasitriangular quasi-Hopf algebra $D(H)$ associated to any quasi-Hopf algebra $H$. The algebra structure is a cocycle double cross product. We use categorical reconstruction methods. As an example, we recover the quasi-Hopf algebra of Dijkgraaf, Pasquier and Roche as the quantum double $D^{\varphi }(G)$ associated to a finite group $G$ and group 3-cocycle $\varphi$.

LATEX 9 pages, final ver. (bit more explicit) as accepted Lett.Math.Phys

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