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Abstract
We give a characterization of indecomposable exceptional modules over finite dimensional gentle algebras. As an application, we study gentle algebras arising from an unpunctured surface and show that a class of indecomposable modules related to curves without self-intersections, as exceptional modules, are uniquely determined by their dimension vectors.
ACKNOWLEDGMENTS
The author is indebted to professor Feng Luo for pointing out Theorem 3.1 when he was giving series of lectures in Mathematical center in Tsinghua University. He is very grateful for professor Thomas Brüstle, professor Bin Zhu and Yu Zhou with many helpful discussions and he also thanks professor Jan Schröer for many helpful comments and for telling him that a conjecture in a previous version of the paper is wrong.
Notes
Communicated by D. Zacharia.
Color versions of one or more of the figures in the articlecan be found online at www.tandfonline.com/lagb.