Toën's formula and Green's formula

Abstract

Let $\mathcal{A}$ be a finitary hereditary abelian category. In this note, we use the associativity of the derived Hall algebra associated to the bounded derived category of $\mathcal{A}$, whose multiplication structure constants are given by the so-called Toën's formula, to give a simple proof of Green's formula associated to Hall algebras.

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