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

Zhan Fa and Yanhua Wang ()
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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

Mathematics, 2025, vol. 13, issue 8, 1-15

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.

Keywords: Hopf algebras; Frobenius algebras; Frobenius coalgebras; bi-Frobenius algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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