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Quantum R-matrices and factorization problems. (English) Zbl 0711.17008

It is well known that there exist connections between the classical r- matrix and certain factorization problems in Lie groups. The authors establish a similar relation between the quantum R-matrix and a certain factorization problem in Hopf algebras. They introduce the notion of factorizable Hopf algebra and prove that the double of a Hopf algebra is a factorizable Hopf algebra. Finally the authors give a definition of dressing transformation in the quantum case.
Reviewer: V.Stukopin

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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