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.

引用

页码：1793 / 1829

页数：37

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