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Rota–Baxter Operators on Cocommutative Weak Hopf Algebras

Author

Listed:
  • Zhongwei Wang

    (School of Mathematics, Southeast University, Nanjing 211189, China)

  • Zhen Guan

    (Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China)

  • Yi Zhang

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Liangyun Zhang

    (Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China)

Abstract

In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H . Moreover, we construct a new multiplication “∗” and an antipode S B from a Rota–Baxter operator B on H such that H B = ( H , ∗ , η , Δ , ε , S B ) becomes a new weak Hopf algebra. Finally, all Rota–Baxter operators on a weak Hopf algebra of a matrix algebra are given.

Suggested Citation

  • Zhongwei Wang & Zhen Guan & Yi Zhang & Liangyun Zhang, 2021. "Rota–Baxter Operators on Cocommutative Weak Hopf Algebras," Mathematics, MDPI, vol. 10(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:95-:d:712762
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