Homothetic Rota–Baxter Systems and Dyck$$^m$$-Algebras - Tomasz Brzezinski (Springer Proceedings in Mathematics & Statistics, 2023)
It is shown that generalized Rota–Baxter operators introduced in [W. A. Martinez, E. G. Reyes, M. Ronco, Int. J. Geom. Meth. Mod. Phys. 18, 2150176 (2021)] are a special case of Rota–Baxter systems [T. Brzeziński, J. Algebra 460, 1–25 (2016)]. The latter are enriched by homothetisms and then shown to give examples of Dyck m -algebras.