Abstract
The present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra.
Funding source: Georgian National Science Foundation
Award Identifier / Grant number: ST08/3-387
Funding statement: The research was supported by the grant ST08/3-387 by the Georgian National Science Foundation.
Acknowledgements
The problem solved in this article was proposed by T. Pirashvili in a private friendly conversation.
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