Geodesic
Cohomology of Modules Over $H$-categories and Co-$H$-categories
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1352-1385

Voir la notice de l'article provenant de la source Cambridge

DOI

Let $H$ 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.
DOI : 10.4153/S0008414X19000403
Mots-clés : H-category, co-H-category, H-equivariant module, relative Hopf module 
Balodi, Mamta; Banerjee, Abhishek; Ray, Samarpita. Cohomology of Modules Over $H$-categories and Co-$H$-categories. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1352-1385. doi: 10.4153/S0008414X19000403
@article{10_4153_S0008414X19000403,
     author = {Balodi, Mamta and Banerjee, Abhishek and Ray, Samarpita},
     title = {Cohomology of {Modules} {Over} $H$-categories and {Co-}$H$-categories},
     journal = {Canadian journal of mathematics},
     pages = {1352--1385},
     year = {2020},
     volume = {72},
     number = {5},
     doi = {10.4153/S0008414X19000403},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000403/}
}
TY  - JOUR
AU  - Balodi, Mamta
AU  - Banerjee, Abhishek
AU  - Ray, Samarpita
TI  - Cohomology of Modules Over $H$-categories and Co-$H$-categories
JO  - Canadian journal of mathematics
PY  - 2020
SP  - 1352
EP  - 1385
VL  - 72
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000403/
DO  - 10.4153/S0008414X19000403
ID  - 10_4153_S0008414X19000403
ER  - 
%0 Journal Article
%A Balodi, Mamta
%A Banerjee, Abhishek
%A Ray, Samarpita
%T Cohomology of Modules Over $H$-categories and Co-$H$-categories
%J Canadian journal of mathematics
%D 2020
%P 1352-1385
%V 72
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000403/
%R 10.4153/S0008414X19000403
%F 10_4153_S0008414X19000403

Cité par Sources :