"linear algebraic group" meaning in English

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          "ref": "2003, Igor Dolgachev, Lectures on Invariant Theory, Cambridge University Press, page xiii:",
          "text": "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.",
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        },
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          "ref": "2011, Teresa Crespo, Zbigniew Hajto, Algebraic Groups and Differential Galois Theory, American Mathematical Society, page xi:",
          "text": "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.",
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          "text": "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,\nActions 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."
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        "An algebraic group that is isomorphic to a subgroup of some general linear group."
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        "(algebraic geometry, category theory) An algebraic group that is isomorphic to a subgroup of some general linear group."
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