Vol. 99, No. 2, 1982

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
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