Coloured quivers for rigid objects and partial triangulations: The unpunctured case

Details Coloured quivers for rigid objects and partial triangulations: The unpunctured case Coloured quivers for rigid objects and partial triangulations: The unpunctured case

2010-12-28

arxiv.org/abs/1012.5790v3

Mathematics

Representation Theory

27 pages, 15 figures. Some minor corrections and update of references

Scientific paper

We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi--Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We show that, in the case where the category is the generalised cluster category associated to a surface, the coloured quivers coincide. We also show that compatible notions of mutation can be defined and give an explicit description in the case of a disk. A partial description is given in the general 2-Calabi--Yau case. We show further that Iyama-Yoshino reduction can be interpreted as cutting along an arc in the surface.

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