2024/10/23 by Agustina Czenky, Jacob Kesten, Czenky, Agustina +5 · 1 citation
Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2410.18232
openalex publication_date 2024/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.