An algebraic group is a variety (or scheme) endowed with a group structure such that the group operations are morphisms of varieties (or schemes). The concept is similar to that of a Lie group except that the underlying operations are required to be algebraic (locally representable in terms of polynomials) rather than differentiable. Complex linear groups (e.g., S L(n, C)) are examples of algebraic groups.

free group | group | Lie group