Conjugacy of Cartan subalgebras of complex finite-dimensional Leibniz algebras

In the present work the properties of Cartan subalgebras and their connection with regular elements in finite-dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regu...

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Bibliographic Details
Published in:Journal of algebra 2006-08, Vol.302 (2), p.887-896
Main Author: Omirov, B.A.
Format: Article
Language:English
Subjects:
Cartan subalgebra
Leibniz algebra
Lie algebra
Regular element
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Summary:In the present work the properties of Cartan subalgebras and their connection with regular elements in finite-dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regular elements of a Lie algebra by a natural homomorphism. Conjugacy of Cartan subalgebras of Leibniz algebras is shown.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2006.01.004