On extended Frobenius structures
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914128602333184 |
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| author | Czenky, Agustina Kesten, Jacob Quinonez, Abiel Walton, Chelsea |
| author_facet | Czenky, Agustina Kesten, Jacob Quinonez, Abiel Walton, Chelsea |
| contents | A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006, Turaev and Turner introduced additional structure on Frobenius algebras, forming what are called extended Frobenius algebras, to classify 2-TQFTs in the unoriented case. This work provides a systematic study of extended Frobenius algebras in various settings: over a field, in a monoidal category, and in the framework of monoidal functors. Numerous examples, classification results, and general constructions of extended Frobenius algebras are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On extended Frobenius structures Czenky, Agustina Kesten, Jacob Quinonez, Abiel Walton, Chelsea Quantum Algebra A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006, Turaev and Turner introduced additional structure on Frobenius algebras, forming what are called extended Frobenius algebras, to classify 2-TQFTs in the unoriented case. This work provides a systematic study of extended Frobenius algebras in various settings: over a field, in a monoidal category, and in the framework of monoidal functors. Numerous examples, classification results, and general constructions of extended Frobenius algebras are established. |
| title | On extended Frobenius structures |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2410.18232 |