  For any field $\K$ and integer $n\geq 2$ we consider the Leavitt algebra
$L_\K(n)$; for any integer $d\geq 1$ we form the matrix ring $S =
M_d(L_\K(n))$. $S$ is an associative algebra, but we view $S$ as a Lie algebra
using the bracket $[a,b]=ab-ba$ for $a,b \in S$. We denote this Lie algebra as
$S^-$, and consider its Lie subalgebra $[S^-,S^-]$. In our main result, we show
that $[S^-,S^-]$ is a simple Lie algebra if and only if char$(\K)$ divides
$n-1$ and char$(\K)$ does not divide $d$. In particular, when $d=1$ we get that
$[L_\K(n)^-,L_\K(n)^-]$ is a simple Lie algebra if and only if char$(\K)$
divides $n-1$.
