The Lie algebra structure of $\mathrm{HH}^1(B)$ for blocks with a normal defect group

It is an open question whether the Lie algebra $\mathrm{HH}^1(B)$ of a block of a finite group algebra $kG$ over an algebraically closed field $k$ of prime characteristic $p$ is simple only if the block is nilpotent with an elementary abelian defect group of order at least $3$. We show this to be th