Speaker
Description
Let $A$ be an associative algebra. The Hochschild cohomology of $A$ has a rich structure: it is a Gerstenhaber algebra. In particular, its first degree component, denoted by $\mathrm{HH}^1(A)$ is a Lie algebra. In positive characteristic $\mathrm{HH}^1(A)$ is a restricted Lie algebra.
In the first part of this talk, I will show the invariance, as a restricted Lie algebra, of the first Hochschild cohomology under derived equivalences and under stable equivalences of Morita type for symmetric algebras.
In the second part, I will focus on the relation between the fundamental groups associated to presentations of $A$ and the maximal tori in $\mathrm{HH}^1(A)$. As an application, I will show that if two finite dimensional monomial algebras are derived equivalent, then their Gabriel quivers contain the same number of arrows. For gentle algebras, this was proven by Avella-Alaminos and Geiss.
