Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

Abstract

We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions.

References in corpus (7)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• n-ary algebras: a review with applications
• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Fuzzy Riemann Surfaces
• Representation theory of C-algebras for a higher order class of spheres and tori

Cited by in corpus (6)

• Cohomology and Deformations of $n$-Lie algebra morphisms
• A new approach to representations of $3$-Lie algebras and abelian extensions
• Some constructions of multiplicative $n$-ary Hom-Nambu algebras
• 3-ary Hom-Lie superalgebras induced Hom-Lie superalgebras
• Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras
• On Structure and Central Extensions of $(n+1)$-Lie Algebras Induced by $n$-Lie Algebras