Representations of the Generalized Lie Algebra sl(2)_q

Abstract

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra $\ssll (2)_q$ introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic and $q$ at roots of unity. Some of the representations have no classical analog even for generic $q$. Some of the representations have no analog to the finite-dimensional representations of the quantised enveloping algebra $U_q(sl(2))$, while in those that do there are different matrix elements.

14 pages, plain-TEX file using input files harvmac.tex, amssym.def

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• Quantum and Braided Lie Algebras
• SU_q(n) Gauge Theory
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Cited by in corpus (1)

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