👉 In mathematics, a non-reductive group is a type of algebraic variety that admits no proper subvarieties. A group G is called non-reductive if it does not admit any finite subgroups that are normal in G and do not contain trivial normal subgroups. Non-reductive groups are important in the study of Lie algebras, particularly in the context of semisimple Lie algebras and their representations. For example, the group of invertible matrices over a field K is
