Rota-Baxter bialgebra structures arising from (co-)quasi-idempotent elements

Abstract

In this note, we construct Rota-Baxter (coalgebras) bialgebras by (co-)quasi-idempotent elements and prove that every finite dimensional Hopf algebra admits nontrivial Rota-Baxter bialgebra structures and tridendriform bialgebra structures. We give all the forms of (co)-quasi-idempotent elements and related structures of tridendriform (co, bi)algebras and Rota-Baxter (co, bi)algebras on the well-known Sweedler's four-dimensional Hopf algebra.

Keywords

• Rota-Baxter bialgebras
• (co-)quasi-idempotent element
• tridendriform bialgebra

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