François Huard

Tilted string algebras

Abstract In this paper, we shall find some simple combinatorial criteria for a string algebra to be tilted or quasi-tilted. As a consequence, this will enable one to construct a lot of new examples of tilted algebras. We shall also determine all quasi-tilted string algebras which are not tilted.

Tilted gentle algebras

The notion of gentle algebra was introduced by I.Assem and A.Skowronski in [4] when classifying the iterated tilted algebras of type .We classify the tilted gentle algebras and give an easy combinatorial condition allowing to verify whether a gentle algebra is tilted or not.

The recognition of bound quivers using edge-coloured homomorphisms

A bound quiver is a digraph together with a collection of specified directed walks. Given an undirected graph G, and a collection of walks I, the bound quiver recognition problem asks: Is there an orientation of G such that each walk in I is directed? We present a polynomial time algorithm for this problem, and a structural characterization of which trees can be oriented as bound quivers. These results are developed using homomorphisms of edge-coloured graphs. Our work includes a classification of the computational complexity of edge-coloured homomorphism problems where the target is of order at most three.

ONE-POINT EXTENSIONS OF QUASI-TILTED ALGEBRAS BY PROJECTIVES

Quasi-tilted algebras have been introduced as a proper generalization of tilted algebras. We give necessary and sufficient conditions for the one-point extension A[P] to be quasi-tilted when A is a quasi-tilted algebra and P is a projective A-module. This generalizes a recent result of Coelho, Martins and de la Peña.