AbstractConformal blocks are central objects in the study of 2d conformal field theory and vertex operator algebras (VOAs). Indeed, many important problems in VOAs are related to conformal blocks, including modular invariance of VOA characters (the earliest such type of problem is the famous monstrous moonshine conjecture), the construction of tensor categories for VOA representations, the stud...
AbstractA modular tensor category is a non-degenerate ribbon finite tensor category. We will constructribbon factorizable Hopfalgebras whose representation categories are modular tensor categories.Specifically, we give some general constructionmethods of ribbon factorizable Honf algebras. Thenwe use these methods to obtain a family of semisimple ribborfactorizable Hopf algebras and twofamilies ...