Special linear group

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In mathematics, the special linear group SL⁡(n,R) of degree n over a commutative ring R is the group (under matrix multiplication) of the n×n matrices with entries in R and determinant 1. This is a normal subgroup of the general linear group, since it is the kernel of the determinant, viewed as a group homorphism from the general linear group to the multiplicative group of R (that is, R excluding 0 when R is a field). These elements are "special" in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation (since the determinant is polynomial in the entries). When R is the finite field of order q, the notation SL⁡(n,q) is sometimes used.

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