The necessity of (co)unit in nearly Frobenius algebra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911919125823488 |
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| author | Cheng, Zhiyun Lei, Ziyi |
| author_facet | Cheng, Zhiyun Lei, Ziyi |
| contents | In this article, we concern the concept of nearly Frobenius algebra, which corresponds to most 2D-TQFT of which each cobordism admits no critical points of index 0 or 2. We prove that any nearly Frobenius algebra over a principal ideal domain with surjective multiplication and injective comultiplication is indeed a Frobenius algebra. The motivation of this study mainly emanates from the investigation of potential constructions of link homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The necessity of (co)unit in nearly Frobenius algebra Cheng, Zhiyun Lei, Ziyi Geometric Topology Rings and Algebras 16T10, 16S10, 57K18 In this article, we concern the concept of nearly Frobenius algebra, which corresponds to most 2D-TQFT of which each cobordism admits no critical points of index 0 or 2. We prove that any nearly Frobenius algebra over a principal ideal domain with surjective multiplication and injective comultiplication is indeed a Frobenius algebra. The motivation of this study mainly emanates from the investigation of potential constructions of link homology. |
| title | The necessity of (co)unit in nearly Frobenius algebra |
| topic | Geometric Topology Rings and Algebras 16T10, 16S10, 57K18 |
| url | https://arxiv.org/abs/2406.10575 |