Simon Lentner

On Monoidal Autoequivalences of the Category of Yetter-Drinfeld Modules Over a Group: The Lazy Case

An interesting open question is to determine the group of monoidal autoequivalences of the category of Yetter-Drinfeld modules over a finite group G, or equivalently the group of Bigalois objects over the dual of the Drinfeld double DG. In particular one would hope to decompose this group into terms related to monoidal autoequivalences for the group algebra, the dual group algebra, and interaction terms. We report on our progress in this question: We first prove a decomposition of the group of Hopf algebra automorphisms of the Drinfeld double into three subgroups, which reduces in the case G=ℤpn

New large-rank Nichols algebras over nonabelian groups with commutator subgroup Z2

G={\mathbb {Z}_{p}^{n}}

New R-matrices for Small Quantum Groups

to a Bruhat decomposition of GL2n(ℤp)

A decomposition of the Brauer–Picard group of the representation category of a finite group

\text {GL}_{2n}(\mathbb {Z}_{p})

Partially dualized Hopf algebras have equivalent Yetter–Drinfel'd modules

. Secondly, we propose a Künneth-like formula for the Hopf algebra cohomology of DG∗ into three terms and prove partial results in the case of lazy cohomology. We use these results for the calculation of the Brauer-Picard group in the lazy case in Lentner and Priel (2015).