Lie triple systems and Leibniz algebras
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Revaz Kurdiani
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.
References
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Articles in the same Issue
- Frontmatter
- Iterative rational least squares fitting
- Extensions of hom-Lie color algebras
- On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities
- On the solvability of a nonlocal problem for the system of Sobolev-type differential equations with integral condition
- Characterizing realcompact locales via remainders
- Jakimovski–Leviatan operators of Kantorovich type involving multiple Appell polynomials
- Further refinements of generalized numerical radius inequalities for Hilbert space operators
- An alternative transient solution for semi-Markov queuing systems
- On generalized fractional integration by parts formulas and their applications to boundary value problems
- Lie triple systems and Leibniz algebras
- Accessibility on iterated function systems
- Bell–Sheffer exponential polynomials of the second kind
- A study of differential prime rings with involution
- Existence result for nonlinear fractional differential equations with nonlocal fractional integro-differential boundary conditions in Banach spaces
- Inequalities for nonuniform wavelet frames
- Notes on quasi-Frobenius rings
