Euler characteristic of quiver Grassmannians and Ringel-Hall algebras of string algebras

2010/02/16 by Nicolas Poettering, Poettering, Nicolas
Mathematics · Physics and Astronomy · #06B15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1002.3040

openalex publication_date 2010/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Euler characteristics of quiver Grassmannians and quiver flag varieties of tree and band modules and prove their positivity. This generalizes some results by G.C. Irelli [arXiv:0910.2592]. As an application we consider the Ringel-Hall algebra C(A) of some string algebras A and compute in combinatorial terms the products of arbitrary functions in C(A).

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