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Séminaire de Mathématique

Extended Hall Algebras and Localization of Categories

by Prof. Mikhail Gorsky (Max Planck Inst. for Mathematics & IHES)

jeudi 15 février 2018 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Hall algebras play an important role in representation theory, algebraic geometry and combinatorics. The Hall algebra of an exact or a triangulated category captures information about the extensions between objects. We consider twisted and extended Hall algebras of triangulated categories and note that in some cases they are well-defined even when their non-extended counterparts are not. We show that each exact category with weak equivalences with an appropriate extra structure naturally gives rise a twisted extended Hall algebra of its homotopy category. If time permits, we will discuss the relation of this construction to graded quiver varieties and to categorification of modified quantum groups.

Organisé par Maxim Kontsevich
Contact Email: cecile@ihes.fr