Derived Hall Algebras

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dc.creatorToen, B.
dc.date2005-01-21
dc.date2006-04-25
dc.date.accessioned2026-07-07T06:39:19Z
dc.date.available2026-07-07T06:39:19Z
dc.descriptionThe purpose of this work is to define a derived Hall algebra $\mathcal{DH}(T)$, associated to any dg-category $T$ (under some finiteness conditions). Our main theorem states that $\mathcal{DH}(T)$ is associative and unital. It is shown that $\mathcal{DH}(T)$ contains the usual Hall algebra $\mathcal{H}(T)$ 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.
dc.description24 pages. A description of the derived Hall algebra of an hereditary abelian category has been added. Final version, to appear in Duke
dc.identifierhttps://arxiv.org/abs/math/0501343
dc.identifierhttp://arxiv.org/abs/math/0501343
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101034
dc.subjectQuantum Algebra
dc.subjectCategory Theory
dc.titleDerived Hall Algebras
dc.typetext

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