Rota–Baxter mock-Lie bialgebras and related structures.

The aim of this paper is to introduce the notion of Rota–Baxter mock-Lie bialgebras (A , ∘ , δ , K , Q) and their admissibility conditions in terms of dual representations (ρ ∗ , β ∗ , V ∗). 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. [ABSTRACT FROM AUTHOR]