Some algebraic structures about Nijenhuis operators

Abstract

In this paper, we aim to study the basic properties of Nijenhuis operators on coalgebras and present three algebraic structures: Nijenhuis admissible coassociative Yang-Baxter equations (cYBes for short), Nijenhuis 2-cycles and admissible Nijenhuis systems. We also prove that new solutions of cYBes can be obtained by Nijenhuis admissible cYBes. The equivalence between Nijenhuis admissible cYBes and Nijenhuis 2-cycles is given. A new way to construct Nijenhuis operators on coalgebra is provided.