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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Embedding of a Lie algebra into Lie-admissible algebras


Author: Hyo Chul Myung
Journal: Proc. Amer. Math. Soc. 73 (1979), 303-307
MSC: Primary 17A30; Secondary 17A20
DOI: https://doi.org/10.1090/S0002-9939-1979-0518509-8
MathSciNet review: 518509
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Abstract: Let A be a flexible Lie-admissible algebra over a field of characteristic $ \ne $ 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 S contains a classical Cartan subalgebra H which is nil in A and such that $ HH \subseteq S$ and $ [H,R] = 0$. In this case, the multiplication between S and R is determined by linear functionals 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^ - }$.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0518509-8
Keywords: Flexible algebra, Lie-admissible algebra, classical Lie algebra, Cartan subalgebra, Levi-factor
Article copyright: © Copyright 1979 American Mathematical Society