PT Journal
AU de Azcarraga, JA
   Izquierdo, JM
TI On a class of n-Leibniz deformations of the simple Filippov algebras
SO Journal of Mathematical Physics
JI J. Math. Phys.
PY 2011
BP 023521
EP 13pp
VL 52
IS 2
DI 10.1063/1.3553797
LA English
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.
ER