Hochschild cohomology and its algebraic structure

MARIANO SUÁREZ-ALVAREZ

México

Conferencia; Coloquio Latinoamericano de Álgebra; 2019

Universidad Autónoma de México

Gerhard Hochschild constructed in the 1940s a cohomology theoryfor associative algebras, motivated by his previous study of separablealgebras and their derivations and using group cohomology as a model. Thiscohomology theory, which we call today Hoschschild cohomology, is one ofthe main homological invariants that we attach to associative algebras andshows up nowadays in many contexts as an important tool --- representationtheory, non-commutative geometry, deformation theory, among others. In thistalk we will present a brief overview of what Hochschild cohomology is,describe some of the algebraic structures that it supports, present a fewclassical and recent results and show some applications.