在数学中，约化群是幂单根为平凡群的代数群。代数环面与半单代数群都是约化群，一般线性群亦然。

「约化」一词源于下述事实：零特征域上的约化群的线性表示都是完全可约的。

对于李群，以下陈述等价

满足以上任一条件的李群称为约化李群，有时我们也会加上条件。

若一李代数满足条件二至四，称之为约化李代数，这相当于说该李代数的伴随表示是完全可约的。但这并不保证所有有限维线性表示都完全可约。

条件一可以延伸到任意局部域上的情形。

In mathematics, a reductive group is an algebraic group G over an algebraically closed field such that the unipotent radical of G is trivial (i.e., the group of unipotent elements of the radical of G). Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group. More generally, over fields that are not necessarily algebraically closed, a reductive group is a smooth affine algebraic group such that the unipotent radical of G over the algebraic closure is trivial. The intervention of an algebraic closure in this definition is necessary to include the case of imperfect ground fields, such as local and global function fields over finite fields. Algebraic groups over (possibly imperfect) fields k such that the k-unipotent radical is trivial are called pseudo-reductive groups.