Quantum Double and Differential Calculi

Details Quantum Double and Differential Calculi Quantum Double and Differential Calculi

1995-07-07

arxiv.org/abs/q-alg/9507004v2

Mathematics

Quantum Algebra

Revised version with added cohomological analysis. 14 pages, plain tex

Scientific paper

10.1007/BF00312672

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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