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

Apr 3, 2013
22 pages
Published in:
  • J.Math.Phys. 54 (2013) 093510
e-Print:
Report number:
  • IFIC-13-20-,
  • FTUV-2-IV-2013

Citations per year

20162017201802
Abstract: (arXiv)
Two types of higher order Lie \ell-ple systems are introduced in this paper. They are defined by brackets with >3\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 (2n3)(2n-3)-Leibniz algebra \fL with a metric nn-Leibniz algebra \tilde{\fL} by using a 2(n1)2(n-1)-linear Kasymov trace form for \tilde{\fL}. Some specific types of kk-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 =3\ell=3.
Note:
  • 22 pages, no figures
  • higher-order
  • algebra: Lie
  • Leibniz