  Let K be a field of characteristic 0 and L be a G-graded Lie PI-algebra,
where G is a finite group. We define the graded Gelfand-Kirillov dimension of
L. Then we measure the growth of the Z_n-graded polynomial identities of the
Lie algebra of n x n traceless matrices sl_n(K) giving an exact value of its
Z_n-graded Gelfand-Kirillov dimension.
