Maximal tori in HH^1 and the fundamental group(s)

发布时间：2021-10-11 作者：浏览次数：

Speaker:	Lleonard Rubio y Degrassi	DateTime:	2021年10月21日(周四)下午3：00-4：30
Brief Introduction to Speaker: Lleonard Rubio y Degrassi, University of Verona.		Place:	腾讯会议，会议号请联系常浩老师
Abstract:Hochschild cohomology is a fascinating invariant of an associative algebra which possesses a rich structure. The first Hochschild cohomology group HH^1(A) of an algebra A is a Lie algebra, which is a derived invariant of A and, among selfinjective algebras, an invariant under stable equivalences of Morita type. More recently, by studying the closely related algebraic group of outer automorphisms of A, maximal tori have been used to obtain combinatorial derived invariants for gentle algebras and Brauer graph algebras. Beyond this, however, fine Lie theoretic properties of HH^1(A) are not often used. In this talk, I will present joint work with Benjamin Briggs where we provide a number of results. I will show that the maximal tori of HH^1(A) can be used to deduce information about the shape of the Gabriel quiver of A. In addition, I will prove that every maximal torus in HH^1(A) arises as the dual of some fundamental group of A. By combining this, with known invariance results for Hoc...