Strongly Graded Coalgebras and Crossed Coproducts

2019 ◽  
pp. 131-142 ◽  
Author(s):  
S. Dăscălescu ◽  
C. Năstăsescu ◽  
Ş. Raianu
Keyword(s):  
Crossed Coproducts

scholarly journals Finite Hopf-Galois Coextensions, Crossed Coproducts, and Duality

1995 ◽  
Vol 178 (2) ◽  
pp. 400-413 ◽  
Author(s):  
S. Dascalescu ◽  
S. Raianu ◽  
Y.H. Zhang
Keyword(s):  
Crossed Coproducts

Crossed coproducts of hopf algebras

1982 ◽  
Vol 10 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Bertrand I-Peng Lin
Keyword(s):  
Hopf Algebras ◽  
Crossed Coproducts

Hopf Algebra Structure Over Crossed Coproducts

2000 ◽  
Vol 24 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Shuanhong Wang ◽  
Dingguo Wang ◽  
Zhongping Yao
Keyword(s):  
Hopf Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Crossed Coproducts

An extended form of Majid’s double biproduct

2017 ◽  
Vol 16 (04) ◽  
pp. 1750061 ◽  
Author(s):  
Tianshui Ma ◽  
Huihui Zheng
Keyword(s):  
Hopf Algebra ◽  
Sufficient Conditions ◽  
Smash Product ◽  
Algebra Structure ◽  
Module Algebra ◽  
Extended Form ◽  
Linear Map ◽  
Product Algebra ◽  
Necessary And Sufficient ◽  
Crossed Coproducts

Let [Formula: see text] be a bialgebra. Let [Formula: see text] be a linear map, where [Formula: see text] is a left [Formula: see text]-module algebra, and a coalgebra with a left [Formula: see text]-weak coaction. Let [Formula: see text] be a linear map, where [Formula: see text] is a right [Formula: see text]-module algebra, and a coalgebra with a right [Formula: see text]-weak coaction. In this paper, we extend the construction of two-sided smash coproduct to two-sided crossed coproduct [Formula: see text]. Then we derive the necessary and sufficient conditions for two-sided smash product algebra [Formula: see text] and [Formula: see text] to be a bialgebra, which generalizes the Majid’s double biproduct in [Double-bosonization of braided groups and the construction of [Formula: see text], Math. Proc. Camb. Philos. Soc. 125(1) (1999) 151–192] and the Wang–Wang–Yao’s crossed coproduct in [Hopf algebra structure over crossed coproducts, Southeast Asian Bull. Math. 24(1) (2000) 105–113].

Crossed coproducts and cleft coextensions

1996 ◽  
Vol 24 (4) ◽  
pp. 1229-1243 ◽  
Author(s):  
S. Dǎscǎlescu ◽  
G. Militaru ◽  
Ş Raianu
Keyword(s):  
Crossed Coproducts

FS-coalgebras and crossed coproducts

2019 ◽  
Vol 26 (3) ◽  
pp. 381-392
Author(s):  
Yuanyuan Chen ◽  
Zhongwei Wang ◽  
Liangyun Zhang
Keyword(s):  
Hopf Algebra ◽  
Finite Dimensional ◽  
Crossed Coproducts ◽  
Quasitriangular Hopf Algebra

Abstract In this paper, we introduce FS-coalgebras, which provide solutions of FS-equations and also solution of braid equations considered by Caenepeel, Militaru and Zhu. FS-coalgebras are constructed by using FS-equations and Harrison cocycles. As applications, we prove that every bialgebra H is an FS-bialgebra if and only if there is a two-sided integral α in {H^{\ast}} such that {\varepsilon(\alpha)=1} , and we show that the crossed coproduct {H^{R}} introduced by the Harrison cocycle R is an FS-coalgebra when {(H,R)} is a finite-dimensional quasitriangular Hopf algebra or a Long copaired bialgebra.

scholarly journals Twistings, crossed coproducts, and Hopf-Galois coextensions

2003 ◽  
Vol 2003 (69) ◽  
pp. 4325-4345 ◽  
Author(s):  
S. Caenepeel ◽  
Dingguo Wang ◽  
Yanxin Wang
Keyword(s):  
Hopf Algebra ◽  
The Relationship ◽  
Crossed Coproducts

LetHbe a Hopf algebra. Ju and Cai (2000) introduced the notion of twisting of anH-module coalgebra. In this paper, we study the relationship between twistings, crossed coproducts, and Hopf-Galois coextensions. In particular, we show that a twisting of anH-Galois coextension remainsH-Galois if the twisting is invertible.

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