ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT 2-CATEGORIES AND THEIR 2-REPRESENTATIONS

被引：6
|
作者：
MacKaay, Marco [1 ,2 ]
Mazorchuk, Volodymyr [3 ]
Miemietz, Vanessa [4 ]
Zhang, Xiaoting [3 ]
机构：
[1] Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Dept Matemat, P-1049001 Lisbon, Portugal
[2] Univ Algarve, FCT, Dept Matemat, 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
来源：
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2020年 / 19卷 / 06期
基金：
瑞典研究理事会;
关键词：
2-category; simple transitive 2-representation; Green relations; coalgebra; 1-morphism; cotensor product; SIMPLE TRANSITIVE 2-REPRESENTATIONS; REPRESENTATIONS; BIMODULES;
D O I：
10.1017/S1474748018000555
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.
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页码：1793 / 1829
页数：37
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