Zestings of quantum groups
- Autores: Héctor Giovanny Mora Díaz
- Directores de la Tesis: César Neyit Galindo Martínez (dir. tes.), Eric Rowell (codir. tes.)
- Lectura: En la Universidad de los Andes (Colombia) ( Colombia ) en 2025
- Idioma: inglés
- Tribunal Calificador de la Tesis: Erik Backelin (presid.), Julia Plavnik (secret.), Ingo Runkel (voc.)
- Enlaces
- Tesis en acceso abierto en: hdl.handle.net
- Resumen
This thesis develops and applies the theory of zesting, a cohomological construction that modifies the monoidal and braided structures of tensor categories. Originally introduced for fusion categories, zesting is here extended to general tensor categories and applied to modular categories arising from quantum groups and to comodule categories over Hopf algebras, always over algebraically closed fields of characteristic zero. We give an algebraic formulation of associative and braided zesting in the Hopf algebra setting, showing in particular that associative zesting yields coquasi-Hopf algebras. Using modular data and pre-metric groups, we classify braided zestings and derive explicit formulas for the S- and T-matrices. Finally, we present explicit computations for pointed Hopf algebras and Verlinde modular categories, including new examples with non-cyclic grading groups and modular categories not directly realized as subcategories of those coming from quantum groups.
