Flexible Lie-admissible algebras with the solvable radical of A/sup -/ Abelian and Lie algebras with nondegenerate forms
- Univ. of Wisconsin, Madison
If A is a flexible Lie-admissible algebra, then A under the product (xy) = xy - yx is a Lie algebra, denoted by A/sup -/. This paper investigates finite-dimensional, simple, flexible, Lie-admissible algebra A over an algebraically closed field of characteristic zero, for which the solvable radical R of A/sup -/ is Abelian. The technique employed is to view A as a module for a semisimple Lie algebra of derivations, and then to use representation theory to gain information about products in A. In the final section of the paper we construct examples of simple flexible Lie-admissible algebras from Lie algebras with nondegenerate associative symmetric bilinear forms. These examples illustrate the great diversity of algebras which can occur when the assumption that R is Abelian is dropped.
- OSTI ID:
- 6644968
- Report Number(s):
- CONF-8008162-
- Journal Information:
- Hadronic J.; (United States), Vol. 4:2; Conference: 3. workshop on Lie-admissible formulations, Boston, MA, USA, 4 Aug 1980
- Country of Publication:
- United States
- Language:
- English
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