2017/01/05 by Haicheng Zhang, Zhang, Haicheng
Mathematics · #16G20 #17B20 #17B37 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1701.01202
openalex publication_date 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, let \A be a finitary hereditary abelian category with enough projectives. By using the associativity formula of Hall algebras, we give a new and simple proof of the main theorem in \citeYan, which states that the Bridgeland's Hall algebra of 2-cyclic complexes of projective objects in \A is isomorphic to the Drinfeld double Hall algebra of \A. In a similar way, we give a simplification of the key step in the proof of Theorem 4.11 in \citeLP.