Quantum Double and Differential Calculi

F. Bonechi; R. Giachetti; R. Maciocco; E. Sorace; M. Tarlini

doi:10.1007/bf00312672

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arXiv · q-alg/9507004

Quantum Double and Differential Calculi

F. Bonechi·R. Giachetti·R. Maciocco·E. Sorace·M. Tarlini

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Abstract

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is connected to the existence of a particular (n+1)--dimensional representation of the double. An example of bicovariant differential calculus on the non quasitriangular quantum group E_q(2) is developed. The construction is studied in terms of Hochschild cohomology and a correspondence between differential calculi and 1-cocycles is proved. Some differences of calculi on quantum and finite groups with respect to Lie groups are stressed.

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F. Bonechi, R. Giachetti, R. Maciocco, E. Sorace, M. Tarlini. 1995-11-18. Quantum Double and Differential Calculi. https://doi.org/10.1007/bf00312672

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