Construction of tilted algebras

Abstract

The finite dimensional algebras of the form End(TA) , where T A is a tilting module, with A a finite dimensional hereditary algebra, are called the tilted algebras. The main interest in tilted algebras comes from the fact that any finite dimensional algebra with a faithful indecomposable module and with Auslander-Reiten quiver without oriented cycle is a tilted algebra. We will recall some properties of tilted algebras in Section 1, but refer for the proofs to [5].