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Nonstandard quantum groups associated to Belavin-Drinfeld triples

Timothy J. Hodges
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Abstract

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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BibTeXRIS

Timothy J. Hodges. 1996-09-23. Nonstandard quantum groups associated to Belavin-Drinfeld triples. https://arxiv.org/abs/q-alg/9609029

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