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

2014/05/22 by Kitouni, Abdennour, Makhlouf, Abdenacer
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1405.5930

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.

Related

• On (n+1)-Hom-Lie Algebras Induced by n-Hom-Lie Algebras
• Lie algebra of an n-Lie algebra
• The Classification of n-Lie Algebras
• Low dimensional nilpotent n-Lie algebras
• Classification of (n+2)-dimensional n-Lie Algebras