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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 1

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

Tianshui Ma(Henan Normal University)0000-0003-1275-7214
Jie Li(Henan Normal University)0000-0003-3931-7569
Haiyan Yang(Henan Normal University)0000-0001-6594-8327
Pages
—
Publication Date
2021-02-04
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Rota-Baxter bialgebras · (co-)quasi-idempotent element · tridendriform bialgebra

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.

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Cite This Article

Ma, T., Li, J., Yang, H. (2021). Rota-Baxter bialgebra structures arising from (co-)quasi-idempotent elements. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 1. https://doi.org/10.15672/hujms.685742

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