special linear group

Definition

The subgroup of the 202406151143 with determinant 1, is called the special linear group

Lie group structure

The determinant function is continuous since it is a polynomial of entries of the matrix. Therefore, if we look at the inverse image of the closed set ,

which is closed. Hence, by the closed subgroup theorem it is a Lie group. (both and )

Lie algebra

Let () denote the Lie algebra of ( respectively).

and