k-Leibniz algebras from lower order ones: from Lie triple to Lie l-ple systems
Apr 3, 201322 pages
Published in:
- J.Math.Phys. 54 (2013) 093510
e-Print:
- 1304.0885 [math-ph]
DOI:
Report number:
- IFIC-13-20-,
- FTUV-2-IV-2013
View in:
Citations per year
Abstract: (arXiv)
Two types of higher order Lie -ple systems are introduced in this paper. They are defined by brackets with 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 -Leibniz algebra \fL with a metric -Leibniz algebra \tilde{\fL} by using a -linear Kasymov trace form for \tilde{\fL}. Some specific types of -Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie -ple generalizations reduce to the standard Lie triple systems for .Note:
- 22 pages, no figures
- higher-order
- algebra: Lie
- Leibniz
References(58)
Figures(0)
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