2007/08/10 by Pavel Etingof, Shlomo Gelaki, Etingof, Pavel +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.CT #math.QA
paper · pdf · doi:10.48550/arxiv.0708.1487
8 pages, latex
openalex publication_date 2007/08/10 · arxiv created 2009/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on symmetric categories of exponential growth, and of Drinfeld on quasitriangular quasi-Hopf algebras. In particular, we classify braided categories of exponential growth which are unipotent, i.e., those whose only simple object is the unit object. We also classify fiber functors on such categories. Finally, using the Etingof-Kazhdan quantization theory of Poisson algebraic groups, we give a classification of coconnected Hopf algebras, i.e. of unipotent categories of exponential growth with a fiber functor.