On tilting modules over cluster-tilted algebras

In this paper, we show that the tilting modules over a cluster-tilted algebra $A$ lift to tilting objects in the associated cluster category ${\mathcal{C}}_H$. As a first application, we describe the induced exchange relation for tilting $A$-modules arising from the exchange relation for tilting object in ${\mathcal{C}}_H$. As a second application, we exhibit tilting $A$-modules having cluster-tilted endomorphism algebras.