New examples of infinite-dimensional n-Lie algebras

Abstract

In this paper we introduce skew-symmetric n-ary brackets on an associative commutative algebra, obtained from Jacobian and Wronskian by adding one more column. For the n-algebras obtained we find the necessary and sufficient conditions to be n-Lie algebras. Thereby we give several new examples of n-Lie algebras. Some of the examples happen to be simple n-Lie algebras.

Keywords:

• n-Lie algebras
• Jacobian
• Wronskian
• simple n-Lie algebra

Acknowledgments

B. Omirov would like to thank the University of California San Diego (USA) for the hospitality under Fulbright Program. The main idea of the paper is a result of some discussions made in UCSD during his visit.

Disclosure statement

No potential conflict of interest was reported by the author(s).