  Quantum Lie algebras are generalizations of Lie algebras which have the
quantum parameter h built into their structure. They have been defined
concretely as certain submodules of the quantized enveloping algebras. On them
the quantum Lie bracket is given by the quantum adjoint action.
  Here we define for any finite-dimensional simple complex Lie algebra g an
abstract quantum Lie algebra g_h independent of any concrete realization. Its
h-dependent structure constants are given in terms of inverse quantum
Clebsch-Gordan coefficients. We then show that all concrete quantum Lie
algebras are isomorphic to an abstract quantum Lie algebra g_h.
  In this way we prove two important properties of quantum Lie algebras: 1) all
quantum Lie algebras associated to the same g are isomorphic, 2) the quantum
Lie bracket of any quantum Lie algebra is $q$-antisymmetric. We also describe a
construction of quantum Lie algebras which establishes their existence.
