Homological properties of piecewise hereditary algebras

Let Λ be a finite dimensional algebra over an algebraically closed field k. We will investigate homological properties of piecewise hereditary algebras Λ. In particular we give lower and upper bounds of the strong global dimension, show the behavior of the strong global dimension under one point extensions and tilting. Moreover we show that the “pieces” of modΛ have Auslander–Reiten sequences.