Quantization of Drinfel'd doubles

Details Quantization of Drinfel'd doubles Quantization of Drinfel'd doubles

2004-11-17

arxiv.org/abs/math/0411389v1

J. Phys. A 38 (2005)

Mathematics

Quantum Algebra

23 pages, no figures

Scientific paper

10.1088/0305-4470/38/18/003

Hopf algebra quantizations of 4-dimensional and 6-dimensional real classical Drinfel'd doubles are studied by following a direct "analytic" approach. The full quantization is explicitly obtained for most of the Drinfel'd doubles, except a small number of them for which the dual Lie algebra is either sl(2) or so(3). In the latter cases, the classical r-matrices underlying the Drinfel'd double quantizations contain known standard ones plus additional twists. Several new four and six-dimensional quantum algebras are presented and some general features of the method are emphasized.

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