2010/09/30 by J. A. de Azcárraga, J. A. de Azcarraga, José Izquierdo +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Class (philosophy) #Infinitesimal #Lie algebra #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Rigidity (electromagnetism) #Simple (philosophy) #hep-th #math-ph #math.MP #math.QA #math.RA
paper · pdf · doi:10.1063/1.3553797
published as J.Math.Phys.52:023521,2011 · 19 pages, 30 refs., no figures. Some text rearrangements for better clarity, misprints corrected. To appear in J. Math. Phys
arxiv created 2011/01/20 · openalex publication_date 2011/02/01 · arxiv updated 2011/10/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.