Tilting modules over an algebra by Igusa, Smalø and Todorov

The finiteness of the little finitistic dimension of an artin algebra R is known to be equivalent to the existence of a tilting R-module T such that where is the category of all finitely presented R-modules of finite projective dimension. Moreover, T can be taken finitely generated if and only if is contravariantly finite. In this paper, we describe explicitly the structure of T for the IST-algebra, a finite-dimensional algebra with not contravariantly finite. We also characterize the indecomposable modules in , and all tilting classes over this algebra.