  It is shown that the dimension of the multilinear quantum Lie operations
space is either equal to zero or included between $(n-2)!$ and $(n-1)!.$ The
lower bound is achieved if the intersection of all conforming subsets is
nonempty, while the upper bound does if all subsets are conforming. We show
that almost always the quantum Lie operations space is generated by symmetric
ones. In particular, the space of all general $n$-linear quantum Lie operations
does. All possible exceptions are described.
