linear algebraic group

linear algebraic group

English

Noun

linear algebraic group (plural linear algebraic groups)

1. (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.

Further reading

• Linear algebraic group on Encyclopedia of Mathematics
• linear algebraic group on nLab