Admissible Yang–Baxter equation for Nijenhuis perm algebras

Abstract

In this paper, on one hand, based on the classical perm Yang–Baxter equation, we investigate under what conditions a perm algebra must be a Nijenhuis perm algebra. On the other hand, we derive the compatible conditions between classical perm Yang–Baxter equation and Nijenhuis operator by a class of Nijenhuis perm bialgebras.