6533b857fe1ef96bd12b4f9b
RESEARCH PRODUCT
k-Leibniz algebras from lower order ones: from Lie triple to Lie l-ple systems
J. A. De AzcárragaJosé M. Izquierdosubject
High Energy Physics - TheoryGeneralized poisson structuresPure mathematicsTrace (linear algebra)SuperalgebrasEquationTriple systemSupertriple systemsOrder (ring theory)FOS: Physical sciencesStatistical and Nonlinear PhysicsLower orderMathematics - Rings and AlgebrasMathematical Physics (math-ph)Nambu mechanicsHigh Energy Physics - Theory (hep-th)Rings and Algebras (math.RA)Mathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)Algebra over a fieldMathematical PhysicsMathematicsBranesdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-09-01 |