International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2005 / Article

Open Access

Volume 2005 |Article ID 580840 | https://doi.org/10.1155/IJMMS.2005.225

N. Z. Iorgov, A. U. Klimyk, "Classification theorem on irreducible representations of the q-deformed algebra Uq(son)", 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 q-deformed algebra Uq(son)

Received08 Aug 2004

Abstract

The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation Uq(son) (which does not coincide with the Drinfel'd-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son()) of the Lie algebra son() when q 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 Uq(son) is proved.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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