A new approach to Rota–Baxter coalgebras
Tom 168 / 2022
Colloquium Mathematicum 168 (2022), 85-104
MSC: Primary 16T05; Secondary 16W99.
DOI: 10.4064/cm8231-7-2020
Opublikowany online: 27 September 2021
Streszczenie
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 are introduced, via Hopf coquasigroup theory and Hopf \pi -algebra theory. In order to do so, the notions of Rota–Baxter linear equation system, Hopf quasicomodule coalgebra, and H_p-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.
