2005/01/21 by Bertrand Toën, B. Toen, Toen, B.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.CT #math.QA
paper · pdf · doi:10.48550/arxiv.math/0501343
24 pages. A description of the derived Hall algebra of an hereditary abelian category has been added. Final version, to appear in Duke
openalex publication_date 2005/01/21 · arxiv created 2006/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this work is to define a derived Hall algebra DH(T), associated to any dg-category T (under some finiteness conditions). Our main theorem states that DH(T) is associative and unital. It is shown that DH(T) contains the usual Hall algebra H(T) when T is an abelian category. We will also prove an explicit formula for the derived Hall numbers purely in terms of invariants of the triangulated category associated to T. As an example, we describe the derived Hall algebra of an hereditary abelian category.