Vol. 86, No. 1, 1980

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Lie algebras and affine algebraic groups

John Henry Reinoehl

Vol. 86 (1980), No. 1, 287–300

For all results obtained, attention is restricted to algebraically closed fields of characteristic zero. An affine algebraic group is said to have property () if the intersection of its center and its radical is unipotent. Given a Lie algebra L, a characterization is obtained of those affine algebraic groups G having property () for which an injection L →ℒ(G) exists whose image is algebraically dense. This is applied to obtain a result concerning the embedding of Lie algebras into algebraic Lie algebras, and to questions about the Hopf algebra of representative functions of a Lie algebra L in the case where L is algebraic.

Mathematical Subject Classification 2000
Primary: 17B45
Received: 21 March 1978
Published: 1 January 1980
John Henry Reinoehl