SL

Given a ring R with identity, the special linear group S L_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group S L_n(q), where q is a prime power, the set of n×n matrices with determinant +1 and entries in the finite field G F(q). S L_n(C) is the corresponding set of n×n complex matrices having determinant +1. S L_n(q) is a subgroup of the general linear group G L_n(q) and is a Lie-type group. Both S L_n(R) and S L_n(C) are genuine Lie groups.

general linear group | special orthogonal group | special unitary group