1. k-Leibniz algebras from lower order ones: from Lie triple to Lie l-ple systems
- Author
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de Azcarraga, J. A. and Izquierdo, J. M.
- Subjects
Mathematical Physics ,High Energy Physics - Theory ,Mathematics - Quantum Algebra ,Mathematics - Rings and Algebras - Abstract
Two types of higher order Lie $\ell$-ple systems are introduced in this paper. They are defined by brackets with $\ell > 3$ 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 $\fL$ with a metric $n$-Leibniz algebra $\tilde{\fL}$ by using a $2(n-1)$-linear Kasymov trace form for $\tilde{\fL}$. Some specific types of $k$-Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie $\ell$-ple generalizations reduce to the standard Lie triple systems for $\ell=3$., Comment: 22 pages, no figures
- Published
- 2013
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