SL

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

general linear group | special orthogonal group | special unitary group