linear algebraic group
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English
[edit]Noun
[edit]linear algebraic group (plural linear algebraic groups)
- (algebraic geometry, category theory) An algebraic group that is isomorphic to a subgroup of some general linear group.
- 2003, Igor Dolgachev, Lectures on Invariant Theory, Cambridge University Press, page xiii:
- Geometric invariant theory arises in an attempt to construct a quotient of an algebraic variety X by an algebraic action of a linear algebraic group G.
- 2011, Teresa Crespo, Zbigniew Hajto, Algebraic Groups and Differential Galois Theory, American Mathematical Society, page xi:
- The differential Galois group of a homogeneous linear differential equation has a structure of linear algebraic group; hence it is endowed, in particular, with the Zariski topology. […] Kolchin used the differential algebra developed by Ritt and also built the foundations of the theory of linear algebraic groups.
- 2015, Willem A. de Graaf, Orbit Closures of Linear Algebraic Groups, Jaime Gutierrez, Josef Schicho, Martin Weimann (editors), Computer Algebra and Polynomials: Applications of Algebra and Number Theory, Springer, LNCS: 8942, page 76,
- Actions of linear algebraic groups appear in many contexts. […] Throughout we assume that the base field is algebraically closed and of characteristic 0, as many constructions that we use (e.g., the correspondence between a linear algebraic group and its Lie algebra) only work well in characteristic 0.