Rota–Baxter paired comodules and Rota–Baxter paired Hopf modules

2021 ◽  
Author(s):  
Huihui Zheng ◽  
Yuxin Zhang ◽  
Liangyun Zhang
Keyword(s):  
Hopf Modules

Separable Functors for the Category of Doi–Hopf Modules II

2019 ◽  
pp. 69-104
Author(s):  
Stefaan Caenepeel ◽  
Bogdan Ion ◽  
Gigel Militaru ◽  
Shenglin Zhu
Keyword(s):  
Hopf Modules

Separable functors for the category of Doi Hom-Hopf modules

2015 ◽  
pp. 1-15
Author(s):  
Shuangjian Guo ◽  
Xiaohui Zhang
Keyword(s):  
Hopf Modules

scholarly journals Cohomology of Modules Over -categories and Co--categories

2019 ◽  
Vol 72 (5) ◽  
pp. 1352-1385
Author(s):  
Mamta Balodi ◽  
Abhishek Banerjee ◽  
Samarpita Ray
Keyword(s):  
Hopf Algebra ◽  
Module Category ◽  
Spectral Sequences ◽  
Locally Finite ◽  
Hopf Module ◽  
Comodule Algebra ◽  
Hopf Modules ◽  
Derived Functors

AbstractLet $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category ${\mathcal{C}}$ as modules over the smash extension ${\mathcal{C}}\#H$. We construct Grothendieck spectral sequences for the cohomologies as well as the $H$-locally finite cohomologies of these objects. We also introduce relative $({\mathcal{D}},H)$-Hopf modules over a Hopf comodule category ${\mathcal{D}}$. These generalize relative $(A,H)$-Hopf modules over an $H$-comodule algebra $A$. We construct Grothendieck spectral sequences for their cohomologies by using their rational $\text{Hom}$ objects and higher derived functors of coinvariants.

The structure theorem and duality theorem for endomorphism algebras of weak Hopf group coalgebras

2017 ◽  
Vol 16 (11) ◽  
pp. 1750208
Author(s):  
Ling Jia
Keyword(s):  
Duality Theorem ◽  
Structure Theorem ◽  
Weak Group ◽  
Endomorphism Algebras ◽  
Hopf Formula ◽  
Hopf Modules ◽  
Homological Algebras

In this paper, we investigate the HOM-functor and state the structure theorem for endomorphism algebras of weak two-sided [Formula: see text]-Hopf [Formula: see text]-modules in order to explore homological algebras for weak Hopf [Formula: see text]-modules, and present the duality theorem for weak group “big” Smash products which extends the result of Menini and Raianu [Morphisms of relative Hopf modules, Smash products and duality, J. Algebra 219 (1999) 547–570] in the setting of weak Hopf group coalgebras.

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

The structure theorem of endomorphism algebras for weak Doi-Hopf modules

2010 ◽  
Vol 127 (3) ◽  
pp. 273-290 ◽  
Author(s):  
R. F. Niu ◽  
Y. Wang ◽  
L. Y. Zhang
Keyword(s):  
Structure Theorem ◽  
Endomorphism Algebras ◽  
Hopf Modules
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