algebraic group

English

Noun

algebraic group (plural algebraic groups)

1. (algebraic geometry) A group that is an algebraic variety.
   • 1998, Martin W. Liebeck, “Introduction to the subgroup structure of algebraic groups”, in Roger William Carter, Meinolf Geck, H. K. Moffatt, editors, Representations of Reductive Groups, Cambridge University Press, page 129:

     The purpose of this article is to discuss various results concerning the subgroups of simple algebraic groups G and of the corresponding finite groups of Lie type G^F (where F is a Frobenius morphism).

   • 1998, Roe Goodman, Nolan R. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press, page 464:

     We begin by showing how to make the quotient of an affine algebraic group by a normal algebraic subgroup into an affine algebraic group, and we determine the structure of commutative affine algebraic groups.

   • 2011, Teresa Crespo, Zbigniew Hajto, Algebraic Groups and Differential Galois Theory, American Mathematical Society, page 75,

     We point out that some properties of an algebraic group are more easily read in its Lie algebra. An important property of an algebraic group is its solvability.

Synonyms

• (group that is an algebraic variety): group variety

Derived terms

• linear algebraic group

Further reading

• Algebraic group on Encyclopedia of Mathematics