A short proof of Green's formula (Q2029190)

Given a finitary hereditary abelian category \(\mathcal {A}\), one can define the Ringel-Hall algebra of \(\mathcal {A}\) and the derived Hall algebra of the bounded derived category \(D^b(\mathcal {A})\) of \(\mathcal {A}\). There is a famous formula on Ringel-Hall numbers, called Green's formula. In the paper under review, the author transforms a certain special derived Hall number to Ringel-Hall number by using the rotation of triangles in \(D^b(\mathcal {A})\). Then he shows that Green's formula is deduced from the associativity of derived Hall algebra.