On the solvability of the Lie algebra $\mathrm{HH}^1(B)$ for blocks of finite groups

Abstract

We give some criteria for the Lie algebra $\mathrm{HH}^1(B)$ to be solvable, where $B$ is a $p$-block of a finite group algebra, in terms of the action of an inertial quotient of $B$ on a defect group of $B$.