  In representation theory, the double centraliser property is an important
property for a module (bimodule). It plays a fundamental role in many theories.
In this paper, we extend this property to complexes in derived categories of
finite dimensional algebras, under the name derived double centraliser
property. Characterizations for complexes with the derived double centraliser
property and (two-sided) tilting complexes in derived categories of hereditary
algebras are given. In particular, all complexes with this property in the
derived categories of lower triangular matrix algebras are classified.
