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Quantization of Drinfel'd doubles

A. Ballesteros·E. Celeghini·M. A. del Olmo
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Abstract

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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A. Ballesteros, E. Celeghini, M. A. del Olmo. 2004-11-17. Quantization of Drinfel'd doubles. https://doi.org/10.1088/0305-4470%2F38%2F18%2F003

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