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- W3101723930 endingPage "012019" @default.
- W3101723930 startingPage "012019" @default.
- W3101723930 abstract "We describe the basic properties of two n-ary algebras, the Generalized Lie Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends the familiar Whitehead's lemma to all $ngeq 2$ FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is no longer required to be fully skewsymmetric one is led to the n-Leibniz (or Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz algebras, those with an anticommutative n-bracket, we study the class of n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first n-1 entires of the n-Leibniz bracket." @default.
- W3101723930 created "2020-11-23" @default.
- W3101723930 creator A5050723897 @default.
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- W3101723930 date "2011-03-01" @default.
- W3101723930 modified "2023-10-18" @default.
- W3101723930 title "Topics on n-ary algebras" @default.
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- W3101723930 doi "https://doi.org/10.1088/1742-6596/284/1/012019" @default.
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