: Astronomy: algebraic group

mathematical technique > algebraic geometry > algebraic variety > algebraic group

algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Algebraic_group)

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