STRUCTURE THEOREMS FOR BICOMODULE ALGEBRAS OVER QUASI-HOPF ALGEBRAS, WEAK HOPF ALGEBRAS, AND BRAIDED HOPF ALGEBRAS

被引：3

作者：

Dello, Jeroen ^{[1
]}

Panaite, Florin ^{[2
]}

Van Oystaeyen, Freddy ^{[3
]}

Zhang, Yinhuo ^{[4
]}

机构：

[1] Univ Hasselt, Dept Math & Stat, Diepenbeek, Belgium

[2] Romanian Acad, Inst Math, POB 1-764, RO-014700 Bucharest, Romania

[3] Univ Antwerp, Dept Math & Comp Sci, Antwerp, Belgium

[4] Univ Hasselt, Dept Math & Stat, Diepenbeek, Belgium

来源：

COMMUNICATIONS IN ALGEBRA | 2016年 / 44卷 / 11期

关键词：

Bicomodule algebra; Braided Hopf algebra; Quasi-Hopf algebra; Weak Hopf algebra; Yetter-Drinfeld module; CROSSED-MODULES; PRODUCTS;

D O I：

10.1080/00927872.2015.1094487

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be a quasi-Hopf algebra, a weak Hopf algebra, or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v : H -> B. Then we can define an object B-co(H), which is a left-left Yetter-Drinfeld module over H, having extra properties that allow to make a smash product B-co(H)#H, which is an H-bicomodule algebra, isomorphic to B.

引用

页码：4609 / 4636

页数：28

共 50 条

[1] Poisson algebras associated to quasi-Hopf algebras
Enriquez, B
Halbout, G
ADVANCES IN MATHEMATICS, 2004, 186 (02) : 363 - 395
[2] Weak Braided Hopf Algebras
Alonso Alvarez, J. N.
Fernandez Vilaboa, J. M.
Gonzalez Rodriguez, R.
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (05) : 2423 - 2458
[3] Categorification and Quasi-Hopf Algebras
Chang Wen-Jing
Wang Zhi-Xi
Wu Ke
Yang Zi-Feng
COMMUNICATIONS IN THEORETICAL PHYSICS, 2011, 56 (02) : 207 - 210
[4] Involutory Quasi-Hopf Algebras
D. Bulacu
S. Caenepeel
B. Torrecillas
Algebras and Representation Theory, 2009, 12 : 257 - 285
[5] THE STRUCTURE THEOREMS OF WEAK HOPF ALGEBRAS
Zhang, Liang-yun
COMMUNICATIONS IN ALGEBRA, 2010, 38 (04) : 1269 - 1281
[6] Involutory Quasi-Hopf Algebras
Bulacu, D.
Caenepeel, S.
Torrecillas, B.
ALGEBRAS AND REPRESENTATION THEORY, 2009, 12 (2-5) : 257 - 285
[7] Categorification and Quasi-Hopf Algebras
常文静
王志玺
吴可
杨紫峰
CommunicationsinTheoreticalPhysics, 2011, 56 (08) : 207 - 210
[8] Relative Hopf modules for (dual) quasi-Hopf algebras
Bulacu, D
Nauwelaerts, E
JOURNAL OF ALGEBRA, 2000, 229 (02) : 632 - 659
[9] Nichols algebras over weak Hopf algebras
WU Zhi-xiang
AppliedMathematics:AJournalofChineseUniversities, 2018, 33 (01) : 107 - 126
[10] COHOMOLOGY OF ALGEBRAS OVER WEAK HOPF ALGEBRAS
Alonso Alvarez, J. N.
Fernandez Vilaboa, J. M.
Gonzalez Rodriguez, R.
HOMOLOGY HOMOTOPY AND APPLICATIONS, 2014, 16 (01) : 341 - 369

← 1 2 3 4 5 →