Faculty Publications

Embedding Of A Lie Algebra Into Lie-Admissible Algebras

Document Type

Article

Keywords

Cartan subalgebra, Classical Lie algebra, Flexible algebra, Levi-factor, Lie-admissible algebra

Journal/Book/Conference Title

Proceedings of the American Mathematical Society

Volume

73

Issue

3

First Page

303

Last Page

307

Abstract

Let A be a flexible Lie-admissible algebra over a field of characteristic ≠ 2, 3. Let S be a finite-dimensional classical Lie subalgebra of A¯ which is complemented by an ideal R of A¯. It is shown that S is a Lie algebra under the multiplication in A and is an ideal of A if and only if 5 contains a classical Cartan subalgebra H which is nil in A and such that HH ⊂ S and [H, R] = 0. In this case, the multiplication between S and R is determined by linear functional on R which vanish on [R, R]. If A is finite-dimensional and of characteristic 0 then this can be applied to give a condition that a Levi-factor S of A¯ be embedded as an ideal into A and to determine the multiplication between S and the solvable radical of A¯. © 1979 American Mathematical Society.

Department

Department of Mathematics

Original Publication Date

1-1-1979

DOI of published version

10.1090/S0002-9939-1979-0518509-8

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