Let \({\cal A}\) be a finitary hereditary abelian category. We define a Hall algebra for the root category of \({\cal A}\) by applying the derived Hall numbers of the bounded derived category \({D^{b}}({\cal A})\) , which is proved to be isomorphic to the Drinfeld double Hall algebra of \({\cal A}\) . In the appendix, we also define the 1-periodic derived Hall algebra via the derived Hall numbers of \({D^{b}}({\cal A})\) .
