%0 Journal Article %T On a class of n-Leibniz deformations of the simple Filippov algebras %A de Azcarraga, J. A. %A Izquierdo, J. M. %J Journal of Mathematical Physics %D 2011 %V 52 %N 2 %I Amer Inst Physics %@ 0022-2488 %G English %F deAzcarraga+Izquierdo2011 %O ISI:000287811800050 %O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=558), last updated on Thu, 25 Aug 2011 10:37:41 +0000 %X 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. %R 10.1063/1.3553797 %U http://arxiv.org/abs/arXiv:1009.2709 %U https://doi.org/10.1063/1.3553797 %P 023521-13pp