Special affine group

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Template:Field-parametrized linear algebraic group

Definition

Let n be a natural number and k be a field. The special affine group or affine special linear group of degree n over k, denoted SA(n,k), SA_n(k), ASL(n,k), or ASL_n(k), is defined as the external semidirect product of the vector space k^n by the special linear group SL(n,k).

It can be viewed as a subgroup of the general affine group, which is the semidirect product of the vector space with the whole general linear group.