dorsal/arxiv
View SchemaQuantum Double and Differential Calculi
| Authors | F. Bonechi, R. Giachetti, R. Maciocco, E. Sorace, M. Tarlini |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507004 |
| URL | https://arxiv.org/abs/q-alg/9507004 |
| DOI | 10.1007/BF00312672 |
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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"abstract": "We show that bicovariant bimodules as defined by Woronowicz are in one to one\ncorrespondence with the Drinfeld quantum double representations. We then prove\nthat a differential calculus associated to a bicovariant bimodule of dimension\nn is connected to the existence of a particular (n+1)--dimensional\nrepresentation of the double. An example of bicovariant differential calculus\non the non quasitriangular quantum group E_q(2) is developed. The construction\nis studied in terms of Hochschild cohomology and a correspondence between\ndifferential calculi and 1-cocycles is proved. Some differences of calculi on\nquantum and finite groups with respect to Lie groups are stressed.",
"arxiv_id": "q-alg/9507004",
"authors": [
"F. Bonechi",
"R. Giachetti",
"R. Maciocco",
"E. Sorace",
"M. Tarlini"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/BF00312672",
"title": "Quantum Double and Differential Calculi",
"url": "https://arxiv.org/abs/q-alg/9507004"
},
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