Quivers with potentials associated to triangulated surfaces, Part II: Arc representations
Abstract
This paper is a representation-theoretic extension of Part I. It has been inspired by three recent developments: surface cluster algebras studied by Fomin-Shapiro-Thurston, the mutation theory of quivers with potentials initiated by Derksen-Weyman-Zelevinsky, and string modules associated to arcs on unpunctured surfaces by Assem-Brustle-Charbonneau-Plamondon. Modifying the latter construction, to each arc and each ideal triangulation of a bordered marked surface we associate in an explicit way a representation of the quiver with potential constructed in Part I, so that whenever two ideal triangulations are related by a flip, the associated representations are related by the corresponding mutation.
Cite
@article{arxiv.0909.4100,
title = {Quivers with potentials associated to triangulated surfaces, Part II: Arc representations},
author = {Daniel Labardini-Fragoso},
journal= {arXiv preprint arXiv:0909.4100},
year = {2009}
}
Comments
51 pages; 37 figures. v2: 52 pages, 37 figures; a reference added; proof of Corollary 6.7 added; minor editorial changes