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., SL(n, C)) are examples of algebraic groups.

free group | group | Lie group