On Structure and Central Extensions of $(n+1)$-Lie Algebras Induced by $n$-Lie Algebras

Abstract

The purpose of this paper is to investigate $(n+1)$-Lie algebras induced by $n$-Lie algebras and trace maps. We highlight a comparison of their structure properties (solvability, nilpotency) and the cohomology groups as well as central extensions. Moreover, we provide for dimensions $n$, $n+1$ and $n+2$, the classification of $n$-Lie algebras which are induced by $(n-1)$-Lie algebras.

arXiv admin note: substantial text overlap with arXiv:1312.7599

References in corpus (3)

• n-ary algebras: a review with applications
• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

Cited by in corpus (3)

• Cohomology and Deformations of $n$-Lie algebra morphisms
• Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras
• On $(n+1)$-Hom-Lie Algebras Induced by $n$-Hom-Lie Algebras