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By using the approach in \cite{XX2006} to Hall algebras arising inhomologically finite triangulated categories, we find an `almost' associativemultiplication structure for indecomposable objects in a 2-periodictriangulated category. As an application, we give a new proof of the theorem ofPeng and Xiao in \cite{PX2000} which provides a way of realizing symmetrizableKac-Moody algebras and elliptic Lie algebras via 2-periodic triangulatedcategories.

Hall algebras associated to triangulated categories, II: almost associativity