Nijenhuis-operator on Hom-Lie conformal algebras

Abstract

The aim of this paper is to study the Nijenhuis operators on Hom-Lie conformal algebras. We construct a graded Lie algebra whose Maurer-Cartan elements are given by Nijenhuis operators with the aid of Frölicher-Nijenhuis bracket. After constructing graded Lie algebra, we define the cohomology associated with a Nijenhuis operator. We further introduce Hom-NS Lie conformal algebra as an algebraic structure behind Nijenhuis operators on Hom-Lie conformal algebra. We provide various examples of Hom-NS Lie conformal algebras. Finally, as an application to cohomology, we study formal deformations of Nijenhuis operators.