Abstract

A 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 of non-semisimple ribbon factorizable Hopf algebras. The representationcategories of thelast two families are prime modular tensor categories, while the representation categories of firstfamily arenot prime modular tensor categories. Finally, we compared their representationcategories with known modular tensorcategories from ribbon factorizable Hopf algebras in somedegree.