QUANTUM LIE-ALGEBRAS ASSOCIATED TO U-Q(GL(N)) AND U-Q(SL(N))

Quantum Lie algebras L(q)(g) are non-associative algebras which are em bedded into the quantized enveloping algebras U-q(g) of Drinfeld and J imbo in the same way as ordinary Lie algebras are embedded into their enveloping algebras. The quantum Lie product on L(q)(g) is induced by the quantum adjoint action of U-q(g). We construct the quantum Lie alg ebras associated to U-q(gl(n)) and U-q(sl(n)). We determine the struct ure constants and the quantum root systems, which are now functions of the quantum parameter q. They exhibit an interesting duality symmetry under q <-> 1/q.