linear algebraic group

plural linear algebraic groups

1. algebraic geometryAn algebraic group that is isomorphic to a subgroup of some general linear group.

   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.

   2003, Igor Dolgachev, Lectures on Invariant Theory, Cambridge University Press, page xiii

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   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.

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

   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.