The Gabriel-Roiter measure for $\widetilde{\mathbb{A}}_n$ II
Representation Theory
2010-09-24 v2
Abstract
Let be a tame quiver of type and the category of finite dimensional representations over an algebraically closed field. A representation is simply called a module. It will be shown that a regular string module has, up to isomorphism, at most two Gabriel-Roiter submodules. The quivers with sink-source orientations will be characterized as those, whose central parts do not contain preinjective modules. It will also be shown that there are only finitely many (central) Gabriel-Roiter measures admitting no direct predecessors. This fact will be generalized for all tame quivers.
Cite
@article{arxiv.0909.5594,
title = {The Gabriel-Roiter measure for $\widetilde{\mathbb{A}}_n$ II},
author = {Bo Chen},
journal= {arXiv preprint arXiv:0909.5594},
year = {2010}
}