algebraic group
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English
Noun
algebraic group (plural algebraic groups)
- (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 GF (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