Torsion Pairs and Rigid Objects in Tubes

被引：0

作者：

Karin Baur

Aslak Bakke Buan

Bethany R. Marsh

机构：

[1] Universität Graz,Institut für Mathematik und wissenschaftliches Rechnen

[2] Norwegian University of Science and Technology,Department of Mathematical Sciences

[3] University of Leeds,School of Mathematics

来源：

Algebras and Representation Theory | 2014年 / 17卷

关键词：

Tube category; Torsion pair; Torsion theory; Pruefer module; Adic module; Annulus; Maximal rigid object; Arc model; Direct limit; Inverse limit; Primary 16G10; 16G70; 55N45; Secondary 13F60; 16G20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Prüfer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.

引用

页码：565 / 591

页数：26

共 30 条

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