IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i3p408-d1327436.html
   My bibliography  Save this article

Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory

Author

Listed:
  • Chuangchuang Kang

    (School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China)

  • Guilai Liu

    (Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China)

  • Zhuo Wang

    (School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300317, China)

  • Shizhuo Yu

    (School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300317, China)

Abstract

A left-Alia algebra is a vector space together with a bilinear map satisfying the symmetric Jacobi identity. Motivated by invariant theory, we first construct a class of left-Alia algebras induced by twisted derivations. Then, we introduce the notions of Manin triples and bialgebras of left-Alia algebras. Via specific matched pairs of left-Alia algebras, we figure out the equivalence between Manin triples and bialgebras of left-Alia algebras.

Suggested Citation

  • Chuangchuang Kang & Guilai Liu & Zhuo Wang & Shizhuo Yu, 2024. "Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:408-:d:1327436
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/3/408/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/3/408/
    Download Restriction: no
    ---><---

    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:12:y:2024:i:3:p:408-:d:1327436. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.