%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