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Quantum deformations of SU(2). (English) Zbl 0715.17017
The author studies finite dimensional representations of two associative algebras: a two-parameter deformation of the universal enveloping algebra of (the complexification of) su(2) (introduced by Curtright and Zachos) and a further one-parameter deformation of the same algebra. This second algebra, introduced in the paper, is expressed in terms of “Cartesian” generators.
In the first case, he constructs analogues of the highest weight modules, parametrized by the positive integers, assuming that the generator corresponding to the Cartan subalgebra is diagonal. In the second case, besides a similar analysis, he constructs a Casimir element and points out a difficulty to define the comultiplication.
Reviewer: N.Andruskiewitsch

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