Nijenhuis Operators on n-Lie Algebras**Supported by National Natural Science Foundation of China under Grant Nos. 11471139, 11271202, 11221091, 11425104, Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20120031110022, and National Natural Science Foundation of Jilin Province under Grant No. 20140520054JH

Abstract

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