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

页码：1 / 33

页数：33

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