Tagged mapping class groups: Auslander-Reiten translation

被引：18

作者：

Bruestle, Thomas ^{[1
]}

Qiu, Yu ^{[1
,2
]}

机构：

[1] Bishops Univ, Sherbrooke, PQ J1M 1Z7, Canada

[2] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway

来源：

MATHEMATISCHE ZEITSCHRIFT | 2015年 / 279卷 / 3-4期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Mapping class group; Auslander-Reiten translation; Triangulated surface; Cluster theory; Braid group; CLUSTER CATEGORIES; ALGEBRAS; QUIVERS;

D O I：

10.1007/s00209-015-1405-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface with marked points and non-empty boundary, which generalizes Brustle-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 associated to the surface and the corresponding Seidel-Thomas braid group of is empty, unless is a polygon with at most one puncture (i.e. of type A or D).

引用

页码：1103 / 1120

页数：18

共 26 条

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