IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1920-d831093.html
   My bibliography  Save this article

The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras

Author

Listed:
  • Shuangjian Guo

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Shengxiang Wang

    (School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China)

  • Xiaohui Zhang

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras. Additionally, we extend the notion of relative Rota–Baxter operators to Hom–Leibniz algebras and prove that there is a Hom–pre-Leibniz algebra structure on Hom–Leibniz algebras that have a relative Rota–Baxter operator. Finally, we study the classical Hom–Leibniz Yang–Baxter equation on Hom–Leibniz algebras and present its connection with the relative Rota–Baxter operator.

Suggested Citation

  • Shuangjian Guo & Shengxiang Wang & Xiaohui Zhang, 2022. "The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras," Mathematics, MDPI, vol. 10(11), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1920-:d:831093
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1920/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1920/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuanyuan Chen & Liangyun Zhang, 2015. "Hom- -Operators and Hom-Yang-Baxter Equations," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-11, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1920-:d:831093. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.