A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements
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 <i>n</i> elements on graded algebra <inline-formula><math xmlns="http://www.w3.org/199...
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2025-04-01
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| author | Zhan Fa Yanhua Wang |
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| description | 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 <i>n</i> elements on graded algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>.</mo></mrow></semantics></math></inline-formula> The comultiplication and counit are defined via a permutation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>,</mo></mrow></semantics></math></inline-formula> such that <i>A</i> becomes a bi-Frobenius algebra. For any <i>n</i>, these bi-Frobenius algebras are neither Hopf algebras nor S-type bi-Frobenius algebras. |
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| spelling | doaj-art-382cb74afd564f808499e89e637e3beb2025-08-20T02:18:04ZengMDPI AGMathematics2227-73902025-04-01138135710.3390/math13081357A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> ElementsZhan Fa0Yanhua Wang1School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, ChinaSchool of Mathematics, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai 200433, ChinaBi-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 <i>n</i> elements on graded algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>.</mo></mrow></semantics></math></inline-formula> The comultiplication and counit are defined via a permutation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mo>,</mo></mrow></semantics></math></inline-formula> such that <i>A</i> becomes a bi-Frobenius algebra. For any <i>n</i>, these bi-Frobenius algebras are neither Hopf algebras nor S-type bi-Frobenius algebras.https://www.mdpi.com/2227-7390/13/8/1357Hopf algebrasFrobenius algebrasFrobenius coalgebrasbi-Frobenius algebras |
| spellingShingle | Zhan Fa Yanhua Wang A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements Mathematics Hopf algebras Frobenius algebras Frobenius coalgebras bi-Frobenius algebras |
| title | A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements |
| title_full | A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements |
| title_fullStr | A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements |
| title_full_unstemmed | A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements |
| title_short | A Class of Non-Hopf Bi-Frobenius Algebras Generated by <i>n</i> Elements |
| title_sort | class of non hopf bi frobenius algebras generated by i n i elements |
| topic | Hopf algebras Frobenius algebras Frobenius coalgebras bi-Frobenius algebras |
| url | https://www.mdpi.com/2227-7390/13/8/1357 |
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