  We present a method to construct new tilting complexes from existing ones
using tensor products, generalizing a result of Rickard. The endomorphism rings
of these complexes are generalized matrix rings that are "componentwise" tensor
products, allowing us to obtain many derived equivalences that have not been
observed by using previous techniques.
  Particular examples include algebras generalizing the ADE-chain related to
singularity theory, incidence algebras of posets and certain Auslander algebras
or more generally endomorphism algebras of initial preprojective modules over
path algebras of quivers. Many of these algebras are fractionally Calabi-Yau
and we explicitly compute their CY dimensions. Among the quivers of these
algebras one can find shapes of lines, rectangles and triangles.
