On Equivalences Between Categories Of Representations

Alexander Zimmermann (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We explain some of the goals of modern representation theory, aiming at categorical methods. We develop one of the most astonishing invariant, Hochschild (co-)homology and we explain on the example of the recent solution of a question due to Rickard how it is possible to reduce fairly abstract questions to explicit methods finally solved by computers.

Mots clés: representations of algebras; derived equivalence; stable equivalence; stable equivalence of Morita type; Hochschild cohomology; Hochschild homology; Gerstenhaber structure; Brauer group

Domaines: Théorie des représentations [math.RT]; K-théorie et homologie [math.KT]; Anneaux et algèbres [math.RA]; Théorie des groupes [math.GR]

Alexander Zimmermann. On Equivalences Between Categories Of Representations. The 8th SEAMS-UGM 2019 Intrenational Congress on Mathematics and its Applications, Jul 2019, Yogyakarta, Indonesia. ⟨hal-02321041⟩