Speaker
Jay Wang
Description
We give some criteria for the Lie algebra of first degree Hochschild cohomology of the twisted group algebra, i.e. $\mathrm{HH}^1(k_\alpha (P\rtimes E))$, to be solvable, where $P$ is a finite abelian $p$-group, $E$ is an abelian $p'$-subgroup of $\mathrm{Aut}(P)$ and $\alpha\in Z^2(E;k^\times)$ inflated to $P\rtimes E$ via the canonical surjection $P\rtimes E\to E$.
As a special case, this gives the criterion to the solvability of the Lie algebra $\mathrm{HH}^1(B)$ where $B$ is a $p$-block of a finite group algebra with abelian defect $P$ and inertial quotient $E$.