Homothetic Rota-Baxter systems and Dyck${}^m$-algebras

Abstract

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 (2021) 2150176] are a special case of Rota-Baxter systems [T. Brzeziński, J. Algebra 460 (2016), 1-25]. The latter are enriched by homothetisms and then shown to give examples of Dyck${}^m$-algebras.

arXiv comment8 pages, submitted to the proceeding of the 14-th International Workshop "Lie Theory and Its Applications in Physics" (LT-14), 21-25 June 2021, Sofia, Bulgaria (on-line)