A short proof of Green's formula
type: Item
instance of: scholarly article
title: A short proof of Green's formula
zbMATH Open document ID: 1476.16011
published in: Journal of Algebra
publication date: 2021-06-03T00:00:00Z
review text: 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.
reviewed by: Haicheng Zhang
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 7354438
zbMATH Keywords: Green's formula
zbMATH Keywords: derived Hall number
zbMATH Keywords: Hall algebra
author: Shiquan Ruan
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2021.04.010
OpenAlex ID: W3154314122
cites work: Hall algebras, hereditary algebras and quantum groups
cites work: Modified Ringel-Hall algebras, Green's formula and derived Hall algebras
cites work: Hall algebras and quantum groups
cites work: Q4875155
cites work: On derived Hall numbers for tame quivers
cites work: Q4981649
cites work: On the double of the Hall algebra of a quiver
cites work: Derived Hall algebras
cites work: Hall algebras associated to triangulated categories
cites work: Toën's formula and Green's formula
DOI: 10.1016/J.JALGEBRA.2021.04.010
description: scientific article; zbMATH DE number 7354438