 
Summary: STRONGLY TILTING TRUNCATED PATH ALGEBRAS
A. Dugas and B. HuisgenZimmermann
Abstract. For any truncated path algebra , we give a structural description of the modules
in the categories P<(mod) and P<(Mod), consisting of the finitely generated (resp.
arbitrary) modules of finite projective dimension. We deduce that these categories are
contravariantly finite in mod and Mod, respectively, and determine the corresponding
minimal P<approximation of an arbitrary module from a projective presentation. In
particular, we explicitly construct based on the Gabriel quiver Q and the Loewy length
of the basic strong tilting module T (in the sense of Auslander and Reiten) which is
coupled with P<(mod) in the contravariantly finite case. A main topic is the study
of the homological properties of the corresponding tilted algebra e = End(T)op, such as
its finitistic dimensions and the structure of its modules of finite projective dimension. In
particular, we characterize, in terms of a straightforward condition on Q, the situation where
the tilting module Te
is strong over e as well. In this esymmetric situation, we obtain
sharp results on the submodule lattices of the objects in P<(Mode), among them a certain
heredity property; it entails that any module in P<(Mode) is an extension of a projective
module by a module all of whose simple composition factors belong to P<(mode).
1. Introduction and terminology
We let = KQ/I be a truncated path algebra of Loewy length L + 1 for some positive
