Ore Extensions for the Sweedler's Hopf Algebra H4

被引：8

作者：

Yang, Shilin ^{[1
]}

Zhang, Yongfeng ^{[1
]}

机构：

[1] Beijing Univ Technol, Sch Math, Fac Sci, Beijing 100124, Peoples R China

来源：

MATHEMATICS | 2020年 / 8卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Ore extension; Drinfeld twist; twisted homomorphism; Hopf algebra; DEFORMATIONS; CLASSIFICATION;

D O I：

10.3390/math8081293

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H-4[z;sigma]of automorphism type for the Sweedler ' s 4-dimensional Hopf algebra H-4. Firstly, we calculate all equivalent classes of twisted homomorphisms (sigma,J) for H-4. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H-4[z;sigma] up to isomorphism.

引用

页数：24

共 22 条

[1] Constructing pointed Hopf algebras by ore extensions [J].

Beattie, M ;

Dascalescu, S ;

Grünenfelder, L .

JOURNAL OF ALGEBRA, 2000, 225 (02) :743-770

[2] Connected Hopf algebras and iterated Ore extensions [J].

Brown, K. A. ;

O'Hagan, S. ;

Zhang, J. J. ;

Zhuang, G. .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (06) :2405-2433

[3]

Davydov A., 2010, Noncommutative structures in mathematics and physics, P103

[4] The classification of triangular semisimple and cosemisimple Hopf algebras over an algebraically closed field [J].

Etingof, P ;

Gelaki, S .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2000, 2000 (05) :223-234

[5]

Etingof P, 2001, MATH RES LETT, V8, P249, DOI 10.4310/MRL.2001.v8.n3.a2

[6] THE CLASSIFICATION OF FINITE-DIMENSIONAL TRIANGULAR HOPF ALGEBRAS OVER AN ALGEBRAICALLY CLOSED FIELD OF CHARACTERISTIC 0 [J].

Etingof, Pavel ;

Gelaki, Shlomo .

MOSCOW MATHEMATICAL JOURNAL, 2003, 3 (01) :37-43

[7] Normal Hopf subalgebras in cocycle deformations of finite groups [J].

Galindo, Cesar ;

Natale, Sonia .

MANUSCRIPTA MATHEMATICA, 2008, 125 (04) :501-514

[8]

Galindo C, 2007, MATH RES LETT, V14, P943, DOI 10.4310/MRL.2007.v14.n6.a4

[9]

McConnell J. C., 1987, Noncommutative Noetherian Rings

[10]

Montgomery S., 1993, CBMS REG C SER MATH, V82

← 1 2 3 →