Faculty Publications

Title

On the construction of reductive Lie-admissible algebras

Document Type

Article

Journal/Book/Conference Title

Journal of Pure and Applied Algebra

Volume

53

Issue

1-2

First Page

75

Last Page

91

Abstract

We discuss a method to construct reductive Lie-admissible algebras which is based on the construction of nonassociative algebras with a specified simple Lie algebra D of derivations. As special cases, we construct two classes of reductive Lie-admissible algebras (A,*) of dimensions 7 and 8 with D=sl(3) and D=G2, and determine their associated reductive Lie algebras g-=A-⊕sl(3) and g-=A-⊕G2. The split octonion, para-octonion, 7-dimensional simple Malcev algebra and simple Lie algebras of type A3, G2, B3 arise from this construction. Representations of simple Lie algebras play a main role. © 1988.

Original Publication Date

1-1-1988

DOI of published version

10.1016/0022-4049(88)90014-X

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