References on $\text{Rep}(H)$ is a braided tensor category There is the statement: > Let $H$ be a Hopf algebra, then $\text{Rep}(H)$ is a braided tensor category. Does anybody know some references on this? Is it covered in Kassel's 'Quantum Groups'?

The correct statement is

> Let $H$ be a quasi-triangular Hopf-algebra, then $\text{Rep}(H)$ is a braided monoidal category.

This statement is covered in Kassel, see proposition XIII 1.4 in his chapter on braided categories. The literal statement is stronger:

> Let $H$ be a bialgebra. Then $\text{Rep}(H)$ is braided if an only if $H$ is a braided algebra (also called a quasi-triangular structure).

The easiest braiding obviously is a flip map. Notice that if $H$ is a cocommutative Hopf-algebra (i.e. the quasi-triangular structure is trivial), then $\text{Rep}(H)$ is trivially braided.