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

Understand

We present an approach of calculating the group of braided autoequivalences of the category of representations of the Drinfeld double of a finite dimensional Hopf algebra $H$ and thus the Brauer-Picard group of $H$-$\mathrm{mod}$.

• We consider two natural subgroups and a subset as candidates for generators.
• In this article $H$ is the group algebra of a finite group $G$.
• As our main result we prove that any element of the Brauer-Picard group, fulfilling an additional cohomological condition, decomposes into an ordered product of our candidates.