From Hopf algebras to tensor categories

TL;DR

This paper surveys spherical Hopf algebras, providing criteria for sphericity, examples, and discussing tilting modules as a method to derive fusion subcategories from their representation categories.

Contribution

It introduces criteria for sphericity in Hopf algebras and explores tilting modules to construct fusion subcategories, advancing understanding of their categorical structures.

Findings

Criteria for sphericity of Hopf algebras

Collection of examples of spherical Hopf algebras

Method to obtain fusion subcategories via tilting modules

Abstract

This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the category of representations of a suitable Hopf algebra.