Cartan Subalgebras of Leibniz n-Algebras

Abstract

The present article is devoted to the investigation of properties of Cartan subalgebras and regular elements in Leibniz n-algebras. The relationship between Cartan subalgebras and regular elements of given Leibniz n-algebra and Cartan subalgebras and regular elements of the corresponding factor n-Lie algebra is established.

Key Words:

• Cartan subalgebra
• Leibniz n-algebra
• n-Lie algebra
• Regular element

2000 Mathematics Subject Classification:

• 17A32
• 17A42
• 17A60

ACKNOWLEDGMENTS

The second and third named authors would like to acknowledge the hospitality of the “Institut für Angewandte Mathematik,” Universität Bonn, Germany. This work is supported in part by the DFG 436 USB 113/10/0-1 project (Germany) and the Fundamental Research Foundation of the Uzbekistan Academy of Sciences. The authors are indebted to the reviewer for very useful remarks and comments.

Notes

Communicated by A. Elduque.