Quasi-idempotent Rota-Baxter operators arising from quasi-idempotent elements

TL;DR

This paper introduces a method to construct quasi-idempotent Rota-Baxter operators from quasi-idempotent elements, demonstrating that finite-dimensional Hopf algebras can have nontrivial Rota-Baxter and tridendriform algebra structures, with concrete examples.

Contribution

It presents a novel construction of quasi-idempotent Rota-Baxter operators and shows their existence in all finite-dimensional Hopf algebras, including quantum groups and Iwahori-Hecke algebras.

Findings

Finite-dimensional Hopf algebras admit nontrivial Rota-Baxter structures.

Construction of quasi-idempotent Rota-Baxter operators from quasi-idempotent elements.

Examples include finite quantum groups and Iwahori-Hecke algebras.

Abstract

In this short note, we construct quasi-idempotent Rota-Baxter operators by quasi-idempotent elements and show that every finite dimensional Hopf algebra admits nontrivial Rota-Baxter algebra structures and tridendriform algebra structures. Several concrete examples are provided, including finite quantum groups and Iwahori-Hecke algebras.