Given a field$k$ and a natural number$n \in \mathbb{N}$, the special linear group$SL(n,k)$ (or $SL_n(k)$) is the subgroup of the general linear group$SL(n,k) \subset GL(n,k)$ consisting of those linear transformations that preserve the volume form on the vector space $k^n$. It can be canonically identified with the group of $n\times n$matrices with entries in $k$ having determinant$1$.