%0 Journal Article
%T k-Leibniz algebras from lower order ones: From Lie triple to Lie l-ple systems
%A de Azcarraga, J. A.
%A Izquierdo, J. M.
%J Journal of Mathematical Physics
%D 2013
%V 54
%N 9
%@ 0022-2488
%F deAzcarraga+Izquierdo2013
%O WOS:000325407300032
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=1618), last updated on Thu, 27 Mar 2014 12:56:22 +0000
%X Two 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.
%R 10.1063/1.4819468
%U http://arxiv.org/abs/1304.0885
%U https://doi.org/10.1063/1.4819468
%P 093510-14pp