Nijenhuis Operators on <i>n</i> -Lie Algebras

Abstract

In this paper, we study $(n-1)$-order deformations of an $n$-Lie algebra and\nintroduce the notion of a Nijenhuis operator on an $n$-Lie algebra, which could\ngive rise to trivial deformations. We prove that a polynomial of a Nijenhuis\noperator is still a Nijenhuis operator. Finally, we give various constructions\nof Nijenhuis operators and some examples.\n