Bi-Frobenius quantum complete intersections with permutation antipodes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917906228445184 |
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| author | Jin, Hai Zhang, Pu |
| author_facet | Jin, Hai Zhang, Pu |
| contents | Quantum complete intersections $A= A({\bf q, a})$ are Frobenius algebras, but in the most cases they can not become Hopf algebras. This paper aims to find bi-Frobenius algebra structures on $A$. A key step is the construction of comultiplication, such that $A$ becomes a bi-Frobenius algebra. By introducing compatible permutation and permutation antipode, a necessary and sufficient condition is found, such that $A$ admits a bi-Frobenius algebra structure with permutation antipode; and if this is the case, then a concrete construction is explicitly given. Using this, intrinsic conditions only involving the structure coefficients $({\bf q, a})$ of $A$ are obtained, for $A$ admitting a bi-Frobenius algebra structure with permutation antipode. When $A$ is symmetric, $A$ admits a bi-Frobenius algebra structure with permutation antipode if and only if there exists a compatible permutation $π$ with $A$ such that $π^2 = {\rm Id}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01485 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bi-Frobenius quantum complete intersections with permutation antipodes Jin, Hai Zhang, Pu Rings and Algebras Quantum complete intersections $A= A({\bf q, a})$ are Frobenius algebras, but in the most cases they can not become Hopf algebras. This paper aims to find bi-Frobenius algebra structures on $A$. A key step is the construction of comultiplication, such that $A$ becomes a bi-Frobenius algebra. By introducing compatible permutation and permutation antipode, a necessary and sufficient condition is found, such that $A$ admits a bi-Frobenius algebra structure with permutation antipode; and if this is the case, then a concrete construction is explicitly given. Using this, intrinsic conditions only involving the structure coefficients $({\bf q, a})$ of $A$ are obtained, for $A$ admitting a bi-Frobenius algebra structure with permutation antipode. When $A$ is symmetric, $A$ admits a bi-Frobenius algebra structure with permutation antipode if and only if there exists a compatible permutation $π$ with $A$ such that $π^2 = {\rm Id}$. |
| title | Bi-Frobenius quantum complete intersections with permutation antipodes |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2309.01485 |