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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/8/1357 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2227-7390 |