Topics on n-ary Algebraic Structures
DOI:
https://doi.org/10.14311/1179Abstract
We review the basic definitions and properties of two types of n-ary structures, the Generalized Lie Algebras (GLA) and the Filippov (≡ n-Lie) algebras (FA), as well as those of their Poisson counterparts, the Generalized Poisson (GPS) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology complexes 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 Whitehead’s lemma to all n ≥ 2, n = 2 being the original Lie algebra case. Some comments onn-Leibniz algebras are also made.
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Published
2010-01-03
How to Cite
Azcárraga, J. A. de, & Izquierdo, J. M. (2010). Topics on n-ary Algebraic Structures. Acta Polytechnica, 50(3). https://doi.org/10.14311/1179
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