de Azcárraga, José A.; Izquierdo, José M. On a class of \(n\)-Leibniz deformations of the simple Filippov algebras. (English) Zbl 1314.17004 J. Math. Phys. 52, No. 2, 023521, 13 p. (2011). Summary: 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. 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