Partial (co)actions of Taft and Nichols Hopf algebras on their base fields

被引：3

作者：

Fonseca, Graziela ^{[1
]}

Martini, Grasiela ^{[2
]}

Silva, Leonardo ^{[3
]}

机构：

[1] Inst Fed Sul Rio Grandense, Pelotas, RS, Brazil

[2] Univ Fed Rio Grande, Rio Grande, RS, Brazil

[3] Univ Fed Rio Grande do Sul, IME, Porto Alegre, RS, Brazil

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2021年 / 31卷 / 07期

关键词：

Partial action; partial coaction; one-dimensional partial (co)representation; Taft algebra; Nichols Hopf algebra; PARTIAL REPRESENTATIONS; ENVELOPING ACTIONS; GLOBALIZATION;

D O I：

10.1142/S0218196721500545

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we determine all partial actions and partial coactions of Taft and Nichols Hopf algebras on their base fields. Furthermore, we prove that all such partial (co)actions are symmetric.

引用

收藏

页码：1471 / 1496

页数：26

相关论文

共 29 条

[1] Partial Hopf module categories [J].

Alvares, Edson R. ;

Alves, Marcelo M. S. ;

Batista, Eliezer .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (08) :1517-1534

[2] GLOBALIZATION OF TWISTED PARTIAL HOPF ACTIONS [J].

Alves, Marcelo M. S. ;

Batista, Eliezer ;

Dokuchaev, Michael ;

Paques, Antonio .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2016, 101 (01) :1-28

[3] Partial corepresentations of Hopf algebras [J].

Alves, Marcelo Muniz S. ;

Batista, Eliezer ;

Castro, Felipe ;

Quadros, Glauber ;

Vercruysse, Joost .

JOURNAL OF ALGEBRA, 2021, 577 :74-135

[4] Dilations of partial representations of Hopf algebras [J].

Alves, Marcelo Muniz S. ;

Batista, Eliezer ;

Vercruysse, Joost .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2019, 100 (01) :273-300

[5] Partial representations of Hopf algebras [J].

Alves, Marcelo Muniz S. ;

Batista, Eliezer ;

Vercruysse, Joost .

JOURNAL OF ALGEBRA, 2015, 426 :137-187

[6]

Alves MMS, 2011, CONTEMP MATH, V537, P13

[7] ENVELOPING ACTIONS FOR PARTIAL HOPF ACTIONS [J].

Alves, Marcelo Muniz S. ;

Batista, Eliezer .

COMMUNICATIONS IN ALGEBRA, 2010, 38 (08) :2872-2902

[8]

[Anonymous], 1979, LIE ALGEBRAS

[9] PARTIAL GROUPOID ACTIONS: GLOBALIZATION, MORITA THEORY, AND GALOIS THEORY [J].

Bagio, Dirceu ;

Paques, Antonio .

COMMUNICATIONS IN ALGEBRA, 2012, 40 (10) :3658-3678

[10] Partial (co)actions of Hopf algebras and partial Hopf-Galois theory [J].

Caenepeel, S. ;

Janssen, K. .

COMMUNICATIONS IN ALGEBRA, 2008, 36 (08) :2923-2946