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Flexible Lie-admissible algebras with the solvable radical of A/sup -/ Abelian and Lie algebras with nondegenerate forms

Conference · · Hadronic J.; (United States)
OSTI ID:6644968
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-
Conference Information:
Journal Name: Hadronic J.; (United States) Journal Volume: 4:2
Country of Publication:
United States
Language:
English

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