New examples of infinite-dimensional n-Lie algebras

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.

Automated summary

In this paper, we introduce skew-symmetric n-ary brackets on an associative commutative algebra and provide several new examples of n-Lie algebras, some of which are simple n-Lie algebras.