Quasi-Frobenius algebras in finite tensor categories
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929234366169088 |
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| author | Shimizu, Kenichi |
| author_facet | Shimizu, Kenichi |
| contents | We introduce the notion of a quasi-Frobenius algebra in a finite tensor category $\mathcal{C}$ and give equivalent conditions for an algebra in $\mathcal{C}$ to be quasi-Frobenius. A quasi-Frobenius algebra in $\mathcal{C}$ is not necessarily Frobenius, however, we show that an algebra $A$ in $\mathcal{C}$ is quasi-Frobenius if and only if $A$ is Morita equivalent to a Frobenius algebra in $\mathcal{C}$. We also show that the class of symmetric Frobenius algebras in $\mathcal{C}$ is closed under the Morita equivalence provided that $\mathcal{C}$ is pivotal so that the symmetricity makes sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-Frobenius algebras in finite tensor categories Shimizu, Kenichi Quantum Algebra Category Theory Rings and Algebras We introduce the notion of a quasi-Frobenius algebra in a finite tensor category $\mathcal{C}$ and give equivalent conditions for an algebra in $\mathcal{C}$ to be quasi-Frobenius. A quasi-Frobenius algebra in $\mathcal{C}$ is not necessarily Frobenius, however, we show that an algebra $A$ in $\mathcal{C}$ is quasi-Frobenius if and only if $A$ is Morita equivalent to a Frobenius algebra in $\mathcal{C}$. We also show that the class of symmetric Frobenius algebras in $\mathcal{C}$ is closed under the Morita equivalence provided that $\mathcal{C}$ is pivotal so that the symmetricity makes sense. |
| title | Quasi-Frobenius algebras in finite tensor categories |
| topic | Quantum Algebra Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2402.02929 |