Simple and semisimple Lie algebras and codimension growth

We study the exponential growth of the codimensions c(n)(L)(B) of a finite dimensional Lie algebra B over a field of characteristic zero. In the case when B is semisimple we show that lim(n-->infinity) (n)root c(n)(L)(B) exis ts and, when F is algebraically closed, is equal to the dimension of the la rgest simple summand of B. As a result we characterize central-simplicity: B is central simple if and only if dim B = lim(n-->infinity) (n)root c(n)(L )(B).