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A Class of Non-Hopf Bi-Frobenius Algebras Generated by n Elements

Author

Listed:
  • Zhan Fa

    (School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Yanhua Wang

    (School of Mathematics, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai 200433, China)

Abstract

Bi-Frobenius algebras are a class of Frobenius algebras and Frobenius coalgebras with some compatible conditions. In this paper, we construct a class of bi-Frobenius algebras generated by n elements on graded algebra A . The comultiplication and counit are defined via a permutation π on A , such that A becomes a bi-Frobenius algebra. For any n , these bi-Frobenius algebras are neither Hopf algebras nor S-type bi-Frobenius algebras.

Suggested Citation

  • Zhan Fa & Yanhua Wang, 2025. "A Class of Non-Hopf Bi-Frobenius Algebras Generated by n Elements," Mathematics, MDPI, vol. 13(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1357-:d:1639255
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