Simple Transitive 2-Representations via (Co-)Algebra 1-Morphisms

被引：19
|
作者：
Mackaay, Marco [1 ,2 ]
Mazorchuk, Volodymyr [3 ]
Miemietz, Vanessa [4 ]
Tubbenhauer, Daniel [5 ,6 ]
机构：
[1] Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Dept Matemat, P-1049001 Lisbon, Portugal
[2] Univ Algarve, Dept Matemat, FCT, Campus Gambelas, P-8005139 Faro, Portugal
[3] Uppsala Univ, Dept Math, Box 480, SE-75106 Uppsala, Sweden
[4] Univ East Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England
[5] Univ Bonn, Math Inst, Endenicher Allee 60,Room 1-003, D-53115 Bonn, Germany
[6] Univ Zurich, Inst Math, Winterthurerstr 190,Campus Irchel,Off Y27J32, CH-8057 Zurich, Switzerland
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2019年 / 68卷 / 01期
基金：
瑞典研究理事会;
关键词：
HOPF-ALGEBRAS; CATEGORIES; BIMODULES;
D O I：
10.1512/iumj.2019.68.7554
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.
引用
收藏
页码：1 / 33
页数：33
相关论文
共 50 条
12345