Euler characteristics of quiver Grassmannians and Ringel-Hall algebras of string algebras.
type: Item
instance of: scholarly article
title: Euler characteristics of quiver Grassmannians and Ringel-Hall algebras of string algebras.
zbMATH Open document ID: 1275.16016
author: Nicolas Haupt
published in: Algebras and Representation Theory
publication date: 2012-12-28T00:00:00Z
review text: The author computes the Euler characteristics of quiver Grassmannians and quiver flag varieties of tree and band modules and proves their positivity. As an application, the author considers the Ringel-Hall algebra \(\mathcal C(A)\) of a string algebra \(A\) and computes, in combinatorial terms, the product of arbitrary functions in \(\mathcal C(A)\). Finally, it is shown that the Euler characteristics of a quiver Grassmannian for some finite dimensional representation of a locally finite quiver is determined by the Euler characteristics of the quiver Grassmannian for a free covering of the corresponding quiver and module.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 14R20
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 6119049
zbMATH Keywords: Euler characteristics
zbMATH Keywords: coverings
zbMATH Keywords: quiver Grassmannians
zbMATH Keywords: flag varieties
zbMATH Keywords: representations
zbMATH Keywords: Ringel-Hall algebras
zbMATH Keywords: string algebras
zbMATH Keywords: band modules
zbMATH Keywords: string modules
zbMATH Keywords: tree modules
MaRDI profile type: Publication
full work available at URL: s10468-010-9264-0
OpenAlex ID: W2065124451
cites work: Q5704250
cites work: On fixed point schemes of actions of multiplicative and additive groups
cites work: Q3999894
cites work: Cluster algebras as Hall algebras of quiver representations.
cites work: From triangulated categories to cluster algebras
cites work: From triangulated categories to cluster algebras II
cites work: Quiver Grassmannians associated with string modules.
cites work: Maps between representations of zero-relation algebras
cites work: Quivers with potentials and their representations II: Applications to cluster algebras
cites work: Cluster algebras. I: Foundations
cites work: Cluster algebras. II: Finite type classification
cites work: Cluster algebras IV: Coefficients
cites work: Q3937542
cites work: Configurations in abelian categories. II: Ringel-Hall algebras
cites work: Kleinian singularities, derived categories and Hall algebras
cites work: Maps between tree and band modules
cites work: Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
cites work: Lie algebras generated by indecomposables
cites work: Canonical bases and moduli spaces of sheaves on curves
cites work: General Representations of Quivers
cites work: Q5423121
DOI: 10.1007/S10468-010-9264-0
description: scientific article; zbMATH DE number 6119049