A CLASSICAL REALIZATION OF QUANTUM ALGEBRAS

Abstract

We construct a realization of a deformation of the Lie algebra of a group in terms of the generators of the classical Lie algebra of the group. The construction works for arbitrary (odd) deforming functions and, as a special case, it reproduces the standard quantum deformation of the algebra. For all these functions it gives a co-multiplication, that is, a group homomorphism, and provides an antipode and a co-unit. It therefore promotes any arbitrary deformation into a Hopf algebra.