TY  - JOUR
AU  - de Azcarraga, J. A.
AU  - Izquierdo, J. M.
PY  - 2011
DA  - 2011//
TI  - On a class of n-Leibniz deformations of the simple Filippov algebras
T2  - J. Math. Phys.
JO  - Journal of Mathematical Physics
SP  - 023521
EP  - 13pp
VL  - 52
IS  - 2
PB  - Amer Inst Physics
AB  - 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.
SN  - 0022-2488
UR  - http://arxiv.org/abs/arXiv:1009.2709
UR  - https://doi.org/10.1063/1.3553797
DO  - 10.1063/1.3553797
LA  - English
N1  - ISI:000287811800050
ID  - deAzcarraga+Izquierdo2011
ER  -