Given a ring 
with identity, the special linear group 
is the group of 
matrices with elements in 
and determinant 1.
The special linear group 
, where 
is a prime power, the set of
matrices with determinant 
and entries in the finite field 
. 
is the corresponding set of 
complex matrices
having determinant 
.
is a subgroup of the general
linear group 
and is a Lie-type group. Both 
and 
are genuine Lie groups.
, 
, 
, and 
." §2.1 in