2-CATEGORIES OF SYMMETRIC BIMODULES AND THEIR 2-REPRESENTATIONS

被引：2
|
作者：
Mazorchuk, Volodymyr [1 ]
Miemietz, Vanessa [2 ]
Zhang, Xiaoting [3 ]
机构：
[1] Uppsala Univ, Dept Math, Uppsala, Sweden
[2] Univ East Anglia, Sch Math, Norwich, Norfolk, England
[3] Capital Normal Univ, Acad Multidisciplinary Studies, Beijing, Peoples R China
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2020年 / 306卷 / 02期
基金：
瑞典研究理事会; 英国工程与自然科学研究理事会;
关键词：
finite abelian group; symmetric bimodule; 2-category; simple transitive 2-representation; CATEGORIES;
D O I：
10.2140/pjm.2020.306.645
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we analyze the structure of 2-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting 2-category is fiat (in the sense of Mazorchuk and Miemietz (2011)) and classify simple transitive 2-representations of this 2-category (under some mild technical assumption). We also study several classes of examples in detail.
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页码：645 / 678
页数：34
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