Fundamental Theorems of Weak Doi–Hopf Modules and Semisimple Weak Smash Product Hopf Algebras

2004 ◽  
Vol 32 (9) ◽  
pp. 3403-3415 ◽  
Author(s):  
Zhang Liangyun ◽  
Zhu Shenglin
Keyword(s):  
Hopf Algebras ◽  
Smash Product ◽  
Hopf Modules ◽  
Weak Smash Product ◽  
Fundamental Theorems

scholarly journals Doi-hopf modules over weak hopf algebras

2000 ◽  
Vol 28 (10) ◽  
pp. 4687-4698 ◽  
Author(s):  
Gabriella Böhm
Keyword(s):  
Hopf Algebras ◽  
Hopf Modules ◽  
Weak Hopf Algebras

Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting

2018 ◽  
Vol 42 (5) ◽  
pp. 2701-2738 ◽  
Author(s):  
J. N. Alonso Álvarez ◽  
J. M. Fernández Vilaboa ◽  
R. González Rodríguez
Keyword(s):  
Hopf Modules ◽  
Fundamental Theorems

On the Hopf algebra dual of an enveloping algebra

1982 ◽  
Vol 91 (2) ◽  
pp. 215-224 ◽  
Author(s):  
Stephen Donkin
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Algebraic Groups ◽  
Field Extension ◽  
Smash Product ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Polycyclic Groups ◽  
Algebra Over A Field

In (1) it is claimed that the main results of that paper have applications to the representation theory of algebraic groups, of polycyclic groups and of Lie algebras. An application to algebraic groups is given in Corollary 6·4 of (1), the applications to polycyclic groups are given in (2), the purpose of this work is to deal with the outstanding case of enveloping algebras. To make use of the results of (1), in this context, we show that the Hopf algebra dual of the enveloping algebra of a finite dimensional Lie algebra over a field of characteristic zero is quasi-affine (see § 1·5). This is done by an easy field extension argument and a generalization, to the Hopf algebra dual of the smash product of Hopf algebras, of Proposition 1·6·3 of (2) on the dual of the group algebra of a semidirect product of groups. Since this paper is aimed at those readers interested in enveloping algebras, the Hopf theoretic aspects are dealt with at a fairly leisurely pace.

Global dimension of weak smash product

2006 ◽  
Vol 7 (12) ◽  
pp. 2088-2092 ◽  
Author(s):  
Ling Jia ◽  
Fang Li
Keyword(s):  
Global Dimension ◽  
Smash Product ◽  
Weak Smash Product

scholarly journals Cobraided smash product Hom-Hopf algebras

2014 ◽  
Vol 134 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Tianshui Ma ◽  
Haiying Li ◽  
Tao Yang
Keyword(s):  
Hopf Algebras ◽  
Smash Product

scholarly journals Relative Hopf Modules for (Dual) Quasi-Hopf Algebras

2000 ◽  
Vol 229 (2) ◽  
pp. 632-659 ◽  
Author(s):  
Daniel Bulacu ◽  
Erna Nauwelaerts
Keyword(s):  
Hopf Algebras ◽  
Hopf Modules

Doi-Hopf modules over Hom-Hopf algebras

2019 ◽  
Vol 13 (8) ◽  
pp. 471-`484
Author(s):  
Chuang Zhou
Keyword(s):  
Hopf Algebras ◽  
Hopf Modules

scholarly journals Doi–Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras

2006 ◽  
Vol 34 (9) ◽  
pp. 3413-3449 ◽  
Author(s):  
D. Bulacu ◽  
S. Caenepeel ◽  
B. Torrecillas
Keyword(s):  
Hopf Algebras ◽  
Drinfeld Modules ◽  
Hopf Modules
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