Yuta Kimura

Let Q be a finite acyclic quiver and w be an element of the Coxeter group of Q.

Buan-Iyama-Reiten-Scott constructed and studied a 2-Calabi-Yau triangulated category E(w).

They showed that, for each reduced expression of w, E(w) has a cluster tilting object.

Amiot -Reiten-Todorov showed that E(w) is triangle equivalent to the cluster category of an algebra A_w.

In this talk, we consider a triangulated category E(w)^Z which is the Z-graded version of E(w).

We show that, for each reduced expression of w, E(w)^Z has a silting object and show a sufficient condition on a reduced expression such that the silting object is a tilting object.

In particular, E(w)^Z is triangle equivalent to the derived category of A_w.