THE STRUCTURE OF QUANTUM LIE-ALGEBRAS FOR THE CLASSICAL SERIES, B-L, C-L AND D-L

The structure constants of quantum Lie algebras depend on a quantum de formation parameter q and they reduce to the classical structure const ants of a Lie algebra at q = 1. We explain the relationship between th e structure constants of quantum Lie algebras and quantum Clebsch-Gord an coefficients for adjoint x adjoint --> adjoint We present a practic al method for the determination of these quantum Clebsch-Gordan coeffi cients and are thus able to give explicit expressions for the structur e constants of the quantum Lie algebras associated to the classical Li e algebras B-l, C-l and D-l. In the quantum case the structure constan ts of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invar iant Killing form on the quantum Lie algebras and find that it takes v alues which are simple q-deformations of the classical ones.