A note on Bridgeland Hall algebras |
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Authors: | Haicheng Zhang |
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Affiliation: | Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, P. R. China |
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Abstract: | 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 proof of the main theorem in [17 Yanagida, S. (2016). A note on Bridgeland’s Hall algebra of two-periodic complexes. Math. Z. 282(3):973–991.[Crossref], [Web of Science ®] , [Google Scholar]], which states that the Bridgeland Hall algebra of 2-cyclic complexes of projective objects in 𝒜 is isomorphic to the Drinfeld double Hall algebra of 𝒜. |
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Keywords: | Bridgeland Hall algebras cyclic complexes Drinfeld double Hall algebras |
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