Hall algebras associated to complexes of fixed size

2019/04/04 by Haicheng Zhang, Zhang, Haicheng
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1904.02400

openalex publication_date 2019/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \A be a finitary hereditary abelian category with enough projectives. We study the Hall algebra of complexes of fixed size over projectives. Explicitly, we first give a relation between Hall algebras of complexes of fixed size and cyclic complexes. Secondly, we characterize the Hall algebra of complexes of fixed size by generators and relations, and relate it to the derived Hall algebra of \A. Finally, we give the integration map on the Hall algebra of 2-term complexes over projectives.

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