On the Lie algebra $\HH^1(B)$ for blocks of finite groups
数学专题报告
报告题目(Title)：On the Lie algebra $\HH^1(B)$ for blocks of finite groups
报告人(Speaker)：王佳琳（City St George's, University of London）
地点(Place)：后主楼1220B
时间(Time)：2025年12月22日（周一）10:00-11:00
邀请人(Inviter)：肖杰、覃帆、周宇、李翼羽
报告摘要
We give some criteria for the Lie algebra of first degree Hochschild cohomology of the twisted group algebra, i.e. $\HH^1(k_\alpha (P\rtimes E))$, to be solvable, where $P$ is a finite abelian $p$-group, $E$ is a $p'$-subgroup of $\Aut(P)$ 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 $\HH^1(B)$ where $B$ is a $p$-block of a finite group algebra with abelian defect $P$ and inertial quotient $E$. We also discuss further about the simplicity of the Lie algebra in this case.
主讲人简介
王佳琳，伦敦大学城市圣乔治学院助理研究员。2024年3月在新加坡南洋理工大学获博士学位。主要研究内容为modular representation theory of finite group algebra，在Journal of London Mathematical Society, Journal of Algebras等知名期刊上发表论文多篇。
