A new approach to Rota–Baxter coalgebras

Abstract

Rota-Baxter algebras are a useful tool applied in many branches of mathematics. However, it is difficult to construct examples of Rota-Baxter coalgebras. In this paper, two new approaches to Rota-Baxter coalgebras of weight −1 are introduced, via Hopf coquasigroup theory and Hopf π-algebra theory. In order to do so, the notions of Rota-Baxter linear equation system, Hopf quasicomodule coalgebra, and Hp-Hopf module coalgebra are introduced and discussed. We present numerous new examples of Rota-Baxter coalgebras. Our ideas of constructing such examples may be viewed as a guide to further development.