  As a natural generalization of ordinary Lie algebras we introduce the concept
of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain
adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a
quantum Lie bracket given by the quantum adjoint action. The structure
constants of these algebras depend on the quantum deformation parameter $q$ and
they go over into the usual Lie algebras when $q=1$.
  The notions of q-conjugation and q-linearity are introduced. q-linear
analogues of the classical antipode and Cartan involution are defined and a
generalised Killing form, q-linear in the first entry and linear in the second,
is obtained. These structures allow the derivation of symmetries between the
structure constants of quantum Lie algebras.
  The explicitly worked out examples of $g=sl_3$ and $so_5$ illustrate the
results.
