Introduction to Quantum Lie Algebras

Abstract

Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in $h$. They are derived from the quantized enveloping algebras $\uqg$. The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. In this paper the recent general results about quantum Lie algebras are introduced with the help of the explicit example of $(s{l}_2{)}_h$.

Contribution to the Proceedings of the Banach Minisemester on Quantum Groups, Warsaw, November 1995. 8 pages amslatex. Files also available at http://www.mth.kcl.ac.uk/~delius/q-lie/qlie_biblio/qlieintr.html

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