Abstract
Given an odd-periodic algebraic triangulated category, we compare Bridgelands Hall algebra in thesense of Bridgeland (2013) and Gorsky (2014), and the derived Hall algebra in the sense of Toen (2006), Xiao and Xu (2008) and Xu and Chen (2013), andshow that the former one is the twisted form of the tensor product of the latter one and a suitable group algebra.
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