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Homothetic Rota–Baxter Systems and Dyck\(^m\)-Algebras

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 396)


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.


  • Rota-Baxter algebra
  • Rota-Baxter system
  • Double homothetism
  • Dyck\(^m\)-algebra

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The research is partially supported by the National Science Centre, Poland, grant no. 2019/35/B/ST1/01115.

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Correspondence to Tomasz Brzeziński .

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Brzeziński, T. (2022). Homothetic Rota–Baxter Systems and Dyck\(^m\)-Algebras. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2021. Springer Proceedings in Mathematics & Statistics, vol 396. Springer, Singapore.

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