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Counting Using Hall Algebras I. Quivers

2011/11/28 by Jiarui Fei, Fei, Jiarui
Mathematics · #13F60 (Secondary) #14D20 #16G20 (Primary) 16T05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1111.6452

openalex publication_date 2011/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey some results on counting the rational points of moduli spaces of quiver representations. We then make generalizations to Grassmannians and flags of quiver representations. These results have nice applications to the cluster algebra. Along the way, we use the full Hopf structure of the Hall algebra of a quiver.

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