@Article{deAzcarraga+Izquierdo2011,
author="de Azcarraga, J. A.
and Izquierdo, J. M.",
title="On a class of n-Leibniz deformations of the simple Filippov algebras",
journal="Journal of Mathematical Physics",
year="2011",
publisher="Amer Inst Physics",
volume="52",
number="2",
pages="023521--13pp",
abstract="We study the problem of infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n > 3 simple finite-dimensional Filippov algebras (FAs) are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n = 2 Filippov (i.e., Lie) algebras. The n = 3 simple FAs, however, admit a nontrivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the n >= 3 simple Filippov algebras do not admit nontrivial central extensions as n-Leibniz algebras of the above class.",
optnote="ISI:000287811800050",
optnote="exported from refbase (https://references.ific.uv.es/refbase/show.php?record=558), last updated on Thu, 25 Aug 2011 10:37:41 +0000",
issn="0022-2488",
doi="10.1063/1.3553797",
opturl="http://arxiv.org/abs/arXiv:1009.2709",
opturl="https://doi.org/10.1063/1.3553797",
archivePrefix="arXiv",
eprint="arXiv:1009.2709",
language="English"
}