On a class of n-Leibniz deformations of the simple Filippov algebras

Sep, 2010
19 pages
Published in:
  • J.Math.Phys. 52 (2011) 023521
e-Print:

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Abstract: (arXiv)
We study the problem of the 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 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 non-trivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the n3n\geq 3 simple Filippov algebras do not admit non-trivial central extensions as n-Leibniz algebras of the above class.
Note:
  • 19 pages, 30 refs., no figures. Some text rearrangements for better clarity, misprints corrected. To appear in J. Math. Phys
  • 02.20.Sv
  • Lie algebras
  • algebra: deformation
  • algebra: Lie
  • cohomology