Vol. 99, No. 2, 1982

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ISSN: 0030-8730
The theory of ad-associative Lie algebras

Richard Cole Penney

Vol. 99 (1982), No. 2, 459–472
Abstract

A Lie algebra is said to be ad-associative if the image of the adjoint representation of on is an associative algebra under composition. We show that every ad-associative Lie algebra is a quotient of a left commutative (xyw = yxw) associative algebra by a Lie ideal. We conclude that every ad-associative Lie algebra is solvable and every irreducible representation of a nilpotent, ad-associative Lie group is square integrable modulo its kernel. We also characterize the HAT algebras of Howe [2] in terms of associative algebra.

Mathematical Subject Classification 2000
Primary: 17B05
Milestones
Received: 15 January 1980
Published: 1 April 1982
Authors
Richard Cole Penney