N. Z. Iorgov, A. U. Klimyk, "Classification theorem on irreducible representations of the -deformed algebra ", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 580840, 38 pages, 2005. https://doi.org/10.1155/IJMMS.2005.225
Classification theorem on irreducible representations of the -deformed algebra
The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard -deformation (which does not coincide with the Drinfel'd-Jimbo quantum algebra ) of the universal enveloping algebra of the Lie algebra when is not a root of unity. These representations are exhausted by irreducible representations of the classical type and of the nonclassical type. The theorem on complete reducibility of finite-dimensional representations of is proved.
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