## Faculty Publications

#### Title

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.

#### Original Publication Date

1-1-1979

#### DOI of published version

10.1090/S0002-9939-1979-0518509-8

#### Recommended Citation

Myung, Hyo Chul, "Embedding of a lie algebra into lie-admissible algebras" (1979). *Faculty Publications*. 4983.

https://scholarworks.uni.edu/facpub/4983