Quantum double and differential calculi |
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Authors: | F Bonechi R Giachetti R Maciocco E Sorace M Tarlini |
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Institution: | (1) Dipartimento di Fisica, Università di Firenze, Italy;(2) Sezione INFN di Firenze, Italy |
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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 nonquasitriangular 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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Keywords: | 16W30 17B37 |
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