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arXiv · 2410.18232

On extended Frobenius structures

Agustina Czenky·Jacob Kesten·Abiel Quinonez·Chelsea Walton
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Abstract

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.

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Agustina Czenky, Jacob Kesten, Abiel Quinonez, Chelsea Walton. 2024-10-23. On extended Frobenius structures. https://arxiv.org/abs/2410.18232

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