On the first relative Hochschild cohomology and contracted fundamental group
数学专题报告
报告题目(Title)：On the first relative Hochschild cohomology and contracted fundamental group
报告人(Speaker)：Lleonard Rubio y Degrassi（Uppsala University）
地点(Place)：北京师范大学后主楼1220报告厅
时间(Time)：2024年8月21日 9:00-10:30
邀请人(Inviter)：刘玉明
报告摘要
In 1956 Hochschild introduced the notion of relative Hochschild cohomology. Years later, Gerstenhaber and Schack used relative Hochschild cohomology in the context of deformation theory. Recently, relative Hochschild cohomology has been used by Cibils, Lanzilotta, Marcos, Schroll and Solotar to describe how the Hochschild cohomology of a bound quiver algebra changes when adding or deleting arrows from the quiver.
Let $A$ be a bound quiver algebra and let $B$ be a subalgebra of $A$ having the same semisimple subalgebra. In this talk, I will give a sufficient condition for the solvability of the first relative Hochschild cohomology HH^1(A|B). One essential ingredient for the proof is the description of the Lie algebra structure of the first relative Hochschild cohomology for radical square zero algebras. To this end, I will describe the combinatorial methods to compute the first relative Hochschild cohomology for monomial algebras using Strametz's work and then we apply these tools to radical square zero algebras.
If time permits, I will also introduce a relative version of the fundamental group of a bound quiver. Similar to the classical case, I will show how these groups are related to the first relative Hochschild cohomology.
This talk is based on joint work with Jonathan Lindell.
主讲人简介
Lleonard Rubio y Degrassi, 瑞典Uppsala大学博士后, 研究方向为同调代数与表示论, 在有限维代数的Hochschild上同调及其李代数结构方面做了许多研究. 相关结果发表在Bulletin of the London Mathematical Society, International Mathematics Research Notices, Pacific Journal of Mathematics等杂志上.
