Nonstandard q-deformation of the universal enveloping algebra $U'({\rm so}_n)$
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- November 1999
- DOI:
- arXiv:
- arXiv:math/9911114
- Bibcode:
- 1999math.....11114K
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory
- E-Print:
- 5 pages, LaTeX