20–22 Sept 2023
Argiletum
Europe/Rome timezone

On the first Hochschild cohomology

20 Sept 2023, 16:00
1h
Argiletum

Argiletum

via della Madonna dei Monti 40, Roma

Speaker

Lleonard Rubio y Degrassi (Uppsala University)

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.

Primary author

Lleonard Rubio y Degrassi (Uppsala University)

Co-author

Dr Benjamin Briggs (University of Copenhagen)

Presentation materials

There are no materials yet.