Quantization of Drinfel'd doubles

A. Ballesteros; E. Celeghini; M.A. del Olmo

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Quantization of Drinfel'd doubles

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arxiv math/0411389 v1 pith:4C3XN26E submitted 2004-11-17 math.QA math.GR

Quantization of Drinfel'd doubles

A. Ballesteros , E. Celeghini , M.A. del Olmo This is my paper

classification math.QA math.GR

keywords drinfeldoublesalgebraclassicaldimensionalquantizationquantizationsadditional

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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.

Quantization of Drinfel'd doubles

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