We study quiver Grassmannians associated with indecomposable representations (of finite dimension) of the Kronecker quiver. We find a cellular decomposition for them and we compute their Betti numbers. As an application, we find a geometric realization for the atomic basis of cluster algebras of type affine-A1 found by Sherman and Zelevinsky (who called it the canonical basis) and those of type affine-A2 found in an earlier paper of the first author.

Geometry of quiver Grassmannians of Kronecker type and applications to cluster algebras / CERULLI IRELLI, Giovanni; Esposito, Francesco. - In: ALGEBRA & NUMBER THEORY. - ISSN 1937-0652. - 5:6(2011), pp. 777-801. [10.2140/ant.2011.5.777]

Geometry of quiver Grassmannians of Kronecker type and applications to cluster algebras

CERULLI IRELLI, GIOVANNI;
2011

Abstract

We study quiver Grassmannians associated with indecomposable representations (of finite dimension) of the Kronecker quiver. We find a cellular decomposition for them and we compute their Betti numbers. As an application, we find a geometric realization for the atomic basis of cluster algebras of type affine-A1 found by Sherman and Zelevinsky (who called it the canonical basis) and those of type affine-A2 found in an earlier paper of the first author.
File allegati a questo prodotto
File Dimensione Formato  
CEsp_ANT_2011.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.89 MB
Formato Adobe PDF
1.89 MB Adobe PDF Visualizza/Apri PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/963780
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 12
social impact