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1 December 2006 Derived Hall algebras
Bertrand Toën
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Duke Math. J. 135(3): 587-615 (1 December 2006). DOI: 10.1215/S0012-7094-06-13536-6

Abstract

The purpose of this work is to define a derived Hall algebra DH(T), associated to any differential graded (DG) category T (under some finiteness conditions), generalizing the Hall algebra of an abelian category. Our main theorem states that DH(T) is associative and unital. When the associated triangulated category [T] is endowed with a t-structure with heart A, it is shown that DH(T) contains the usual Hall algebra H(A). We 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 a hereditary abelian category

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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

Published: 1 December 2006
First available in Project Euclid: 10 November 2006

zbMATH: 1117.18011
MathSciNet: MR2272977
Digital Object Identifier: 10.1215/S0012-7094-06-13536-6

Subjects:
Primary: 18G55

Rights: Copyright © 2006 Duke University Press

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Vol.135 • No. 3 • 1 December 2006
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