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Nonstandard q-deformation of the universal enveloping algebra $U'({\rm so}_n)$

A. U. Klimyk
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Abstract

We describe properties of the nonstandard q-deformation $U'_q({\rm so}_n)$ of the universal enveloping algebra $U({\rm so}_n)$ of the Lie algebra ${\rm so}_n$ which does not coincide with the Drinfeld--Jimbo quantum algebra $U_q({\rm so}_n)$. Irreducible representations of this algebras for q a root of unity q^p=1 are given. These representations act on p^N-dimensional linear space (where N is a number of positive roots of the Lie algebra ${\rm so}_n$) and are given by $r={\rm dim} {\rm so}_n$ complex parameters.

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BibTeXRIS

A. U. Klimyk. 1999-11-16. Nonstandard q-deformation of the universal enveloping algebra $U'({\rm so}_n)$. https://arxiv.org/abs/math/9911114

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