"Let F be a field of characteristic 0, and let F be a finite dimensional vector space over F. Let E denote the algebra of all endomorphisms of V, and let L be any Lie subalgebra of E. Among the algebraic Lie algebras contained in E and containing L, there is one that is contained in all of them, and this is called the algebraic hull of L in E. Here, an algebraic Lie algebra is defined as the Lie algebra of an algebraic group. It is an easy consequence of the definitions that if A and B are algebraic groups of automorphisms of V such that A⊂B then the Lie algebra of A is contained in the Lie algebra of B. Hence the existence of the algebraic hull of L is an immediate consequence of the following basic result: let G be the intersection of all algebraic groups of automorphisms of V whose Lie algebras contain L."
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Academics from the United StatesJews from the United StatesMathematicians from the United StatesMathematicians from GermanyJews from Germany
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Gerhard Hochschild
Gerhard Paul Hochschild (April 29, 1915 – July 8, 2010) was a German-born American mathematician, who did research on Lie groups, algebraic groups, homological algebra and algebraic number theory. He is known for Hochschild homology. In 1979 he was elected to United States National Academy of Sciences.
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