, Volume 10, Issue 1, pp 63-69

Aq-difference analogue of U(g) and the Yang-Baxter equation

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Abstract

Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied to determine the eigenvalues of the trigonometric solution of the Yang-Baxter equation related to sl(2) in an arbitrary finite-dimensional irreducible representation.