arXiv subjects
Publications and source records attributed to Helene R. Tyler.
For an indecomposable module $M$ over a path algebra of a quiver of type $\widetilde{\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic and final parts. We describe how these invariants for $M$ and for its dual specify the position of $M$ in the Auslander-Reiten quiver of the algebra.
This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix.