A note on the generalised Lie algebra sl(2)q

Abstract

In a recent paper, V. Dobrev and A. Sudbery classified the highest-weight and lowest-weight finite dimensional irreducible representations of the quantum Lie algebra sl(2)_q introduced by V. Lyubashenko and A. Sudbery. The aim of this note is to add to this classification all the finite dimensional irreducible representations which have no highest weight and/or no lowest weight, in the case when q is a root of unity. For this purpose, we give a description of the enlarged centre.

Latex2e, 7 pages

References in corpus (4)

• Quantum and Braided Lie Algebras
• On Quantum Lie Algebras and Quantum Root Systems
• Scasimir operator, Scentre and Representations of U_q(osp(1|2))
• Representations of the Generalized Lie Algebra sl(2)_q