Double Hall algebras and derived equivalences

We show that the reduced Drinfeld double of the Ringel–Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of Burban and Schiffmann [5,6], Sevenhant and Van den Bergh (1999) [25], , and Xiao and Yang (2001) [31].