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

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

1998-04-28

arxiv.org/abs/math/9804131v1

J. Phys. A31 (1998) 6647

Mathematics

Quantum Algebra

Latex2e, 7 pages

Scientific paper

10.1088/0305-4470/31/31/011

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.

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