Nonstandard q-deformation of the universal enveloping algebra $U^{\prime }({\mathrm{so}}_n)$

Abstract

We describe properties of the nonstandard q-deformation $U_q^{\prime }({\mathrm{so}}_n)$ of the universal enveloping algebra $U({\mathrm{so}}_n)$ of the Lie algebra ${\mathrm{so}}_n$ which does not coincide with the Drinfeld--Jimbo quantum algebra $U_q({\mathrm{so}}_n)$. 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 ${\mathrm{so}}_n$) and are given by $r=\dim {\mathrm{so}}_n$ complex parameters.

5 pages, LaTeX