dorsal/arxiv
View SchemaNonstandard quantum groups associated to Belavin-Drinfeld triples
| Authors | Timothy J. Hodges |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9609029 |
| URL | https://arxiv.org/abs/q-alg/9609029 |
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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"abstract": "A construction is given of a family of non-standard quantizations of the\nalgebra of functions on a connected complex semi-simple algebraic group. For\neach ``disjoint\u0027\u0027 triple in the sense of Belavin and Drinfeld, a 2-cocycle is\nconstructed on certain multi-parameter quantum groups. The new non-standard\nquantum groups are the Hopf algebras obtained by twisting the known quantum\ngroups by these 2-cocycles. In particular, the Cremmer-Gervais quantization of\n$SL(3)$ can be constructed in this way.",
"arxiv_id": "q-alg/9609029",
"authors": [
"Timothy J. Hodges"
],
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"q-alg",
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"title": "Nonstandard quantum groups associated to Belavin-Drinfeld triples",
"url": "https://arxiv.org/abs/q-alg/9609029"
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