Lie algebra structure of the rst Hochschild cohomology space of gentle algebras and Brauer graph algebras

C. CHAPARRO ACOSTA; S. SCHROLL; A. SOLOTAR

Montpellier

Seminario; Seminaire AGATA, Universite de Montpellier, Francia; 2020

In this talk I will explain how to determine the first Hochschild homology and cohomology spacesof a gentle algebra in terms of the associated quiver and the relations. This leads to an explicitdescription of the Lie algebra structure of the first Hochschild cohomology space of special biserialalgebras (and hence of Brauer graph algebras with multiplicity one in each vertex) based on theHochschild cohomology of trivial extensions of gentle algebras.