Some algebraic structures about Nijenhuis operators

Tianshui Ma, Mengqi Li, Huihui Zheng, Xiaofan Zhao


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.


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