English

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

Quantum Algebra 2007-05-23 v1 Representation Theory

Abstract

We describe properties of the nonstandard q-deformation Uq(son)U'_q({\rm so}_n) of the universal enveloping algebra U(son)U({\rm so}_n) of the Lie algebra son{\rm so}_n which does not coincide with the Drinfeld--Jimbo quantum algebra Uq(son)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 son{\rm so}_n) and are given by r=dimsonr={\rm dim} {\rm so}_n complex parameters.

Keywords

Cite

@article{arxiv.math/9911114,
  title  = {Nonstandard q-deformation of the universal enveloping algebra $U'({\rm so}_n)$},
  author = {A. U. Klimyk},
  journal= {arXiv preprint arXiv:math/9911114},
  year   = {2007}
}

Comments

5 pages, LaTeX