Abstract
The purpose of this work is to define a derived Hall algebra , associated to any differential graded (DG) category (under some finiteness conditions), generalizing the Hall algebra of an abelian category. Our main theorem states that is associative and unital. When the associated triangulated category is endowed with a t-structure with heart , it is shown that contains the usual Hall algebra . We also prove an explicit formula for the derived Hall numbers purely in terms of invariants of the triangulated category associated to . As an example, we describe the derived Hall algebra of a hereditary abelian category
Citation
Bertrand Toën. "Derived Hall algebras." Duke Math. J. 135 (3) 587 - 615, 1 December 2006. https://doi.org/10.1215/S0012-7094-06-13536-6
Information