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.

引用

页码：645 / 678

页数：34

共 50 条

[21] Pyramids and 2-representations
Mazorchuk, Volodymyr
Miemietz, Vanessa
Zhang, Xiaoting
REVISTA MATEMATICA IBEROAMERICANA, 2020, 36 (02) : 387 - 405
[22] 2-CATEGORIES OF SHEAVES
PATNAIK, SN
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (03): : 584 - &
[23] DOCTRINES ON 2-CATEGORIES
ZOBERLEIN, V
MATHEMATISCHE ZEITSCHRIFT, 1976, 148 (03) : 267 - 279
[24] Monoidal categories and monoidal 2-categories
不详
NON-SEMISIMPLE TOPOLOGICAL QUANTUM FIELD THEORIES FOR 3-MANIFOLDS WITH CORNERS, 2002, 1765 : 217 - 259
[25] 2-CATEGORIES AND 2-KNOTS
FISCHER, JE
DUKE MATHEMATICAL JOURNAL, 1994, 75 (02) : 493 - 526
[26] Absolute lax 2-categories
Grandis, Marco
APPLIED CATEGORICAL STRUCTURES, 2006, 14 (03) : 191 - 214
[27] Nerves of 2-categories and 2-categorification of (∞, 2)-categories
Ozornova, Viktoriya
Rovelli, Martina
ADVANCES IN MATHEMATICS, 2021, 391
[28] Locating reaction with 2-categories
Sassone, V
Sobocinski, P
THEORETICAL COMPUTER SCIENCE, 2005, 333 (1-2) : 297 - 327
[29] Group actions on 2-categories
Bernaschini, Eugenia
Galindo, Cesar
Mombelli, Martin
MANUSCRIPTA MATHEMATICA, 2019, 159 (1-2) : 81 - 115
[30] YONEDA STRUCTURES ON 2-CATEGORIES
STREET, R
WALTERS, R
JOURNAL OF ALGEBRA, 1978, 50 (02) : 350 - 379

← 1 2 3 4 5 →