Nonstandard quantum groups associated to Belavin-Drinfeld triples

Details Nonstandard quantum groups associated to Belavin-Drinfeld triples Nonstandard quantum groups associated to Belavin-Drinfeld triples

1996-09-23

arxiv.org/abs/q-alg/9609029v1

Mathematics

Quantum Algebra

AMSLatex, 8 pages

Scientific paper

A construction is given of a family of non-standard quantizations of the algebra of functions on a connected complex semi-simple algebraic group. For each ``disjoint'' triple in the sense of Belavin and Drinfeld, a 2-cocycle is constructed on certain multi-parameter quantum groups. The new non-standard quantum groups are the Hopf algebras obtained by twisting the known quantum groups by these 2-cocycles. In particular, the Cremmer-Gervais quantization of $SL(3)$ can be constructed in this way.

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