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k-Leibniz algebras from lower order ones: From Lie triple to Lie l-ple systems

AuthorsAzcárraga, José A. de ; Izquierdo, José Manuel
KeywordsGeneralized poisson structures
Nambu mechanics
Supertriple systems
Issue Date1-Sep-2013
PublisherAmerican Institute of Physics
CitationJournal of Mathematical Physics 54 (9): 093510 - 14 (2013)
AbstractTwo types of higher order Lie l-ple systems are introduced in this paper. They are defined by brackets with l > 3 arguments satisfying certain conditions, and generalize the well-known Lie triple systems. One of the generalizations uses a construction that allows us to associate a (2n - 3)-Leibniz algebra pound with a metric n-Leibniz algebra () pound over tilde by using a 2(n - 1)-linear Kasymov trace form for () pound over tilde. Some specific types of k-Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie l-ple generalizations reduce to the standard Lie triple systems for l = 3.
Publisher version (URL)http://dx.doi.org/10.1063/1.4819468
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