2012/12/31 by Thomas Brüstle, Yu Qiu · 1 citation
Mathematics · #math.RT #math.GT
paper · pdf · doi:10.1007/s00209-015-1405-z
published as Math. Zeit., 279 (2015), pp 1103-1120 · To appear in Mathematische Zeitschrift
arxiv created 2014/11/05 · arxiv updated 2015/05/27
We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface S with marked points and non-empty boundary, which generalizes Brüstle-Zhang's result for the puncture free case. As an application, we show that the intersection of the shifts in the 3-Calabi-Yau derived category D(ΓS) associated to the surface and the corresponding Seidel-Thomas braid group of D(ΓS) is empty, unless S is a polygon with at most one puncture (i.e. of type A or D).