# Diplomarbeit Karolina Vocke 24.12.2010

**To answer a question of Prof. Christandl about classifying S _{n}-anyonmodels** in the joint-faculty seminar "Quantum Computing" I aimed to explicitely and systematically describe the

**fusion rules**of the Mod-category over the

**twisted Drinfel'd double D**by generalizing Yetter-Drinfel'd modules (action just projective) and characters (now covariantly from G to G).

^{w}(G)**Karolina Vocke** has worked this out as her diploma thesis, which I had the chance to **co-supervise**, in great detail and for many small examples. We're currently working on a publication. It is now save to say, that the knowledge of conjugacy class fusion rules together with the centralizers projective representation theory easily allows to **describe the emerging fusion ring explicitely**.

Especially there seems to be an **astonishing connection** to pointed Hopf algebras: **Proper deformability** of a groupring (i.e. the simple objects change with an appropriate 3-cocycle) **excludes finite dimensional pointed Hopf algebras** in all examples we checked so far. The opposite direction is hereby easily disproven by one family of groups of order p^{3}!