Rota–Baxter mock-Lie bialgebras and related structures

Abstract

The aim of this paper is to introduce the notion of Rota–Baxter mock-Lie bialgebras [Formula: see text] and their admissibility conditions in terms of dual representations [Formula: see text]. Next, we show that Rota–Baxter mock-Lie bialgebras are characterized by matched pairs and Manin triples of Rota–Baxter mock-Lie algebras. Furthermore, the coboundary case leads to the introduction of the admissible mock-Lie Yang–Baxter equation in Rota–Baxter mock-Lie algebras, whose skew-symmetric solutions are used to construct Rota–Baxter mock-Lie bialgebras.