Drinfeld doubles via derived Hall algebras and Bridgeland Hall algebras

Abstract

Let A be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev's theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of A via its derived Hall algebra and Bridgeland Hall algebra of m-cyclic complexes.