Definition:Special Linear Group

Definition
Let $K$ be a field whose zero is $0_K$ and unity is $1_K$.

The set of all order-$n$ square matrices over $K$ whose determinant is $1_K$ is a group under (conventional) matrix multiplication.

The field itself is usually $\R$, $\Q$ or $\C$, but can be any field.

This group is called the Special Linear Group order $n$ on $K$.

It is denoted $\operatorname{SL} \left({n, K}\right)$, or $\operatorname{SL} \left({n}\right)$ if the field is implicit.

Also see

 * Special Linear Group Subgroup of General Linear Group