TY  - JOUR
AU  - de Azcarraga, J. A.
AU  - Izquierdo, J. M.
PY  - 2013
DA  - 2013//
TI  - k-Leibniz algebras from lower order ones: From Lie triple to Lie l-ple systems
T2  - J. Math. Phys.
JO  - Journal of Mathematical Physics
SP  - 093510
EP  - 14pp
VL  - 54
IS  - 9
AB  - 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.
SN  - 0022-2488
UR  - http://arxiv.org/abs/1304.0885
UR  - https://doi.org/10.1063/1.4819468
DO  - 10.1063/1.4819468
N1  - WOS:000325407300032
ID  - deAzcarraga+Izquierdo2013
ER  -