Centralizer theorems for Hopf type Galois extensions
✍ Scribed by Yoichi Miyashita
- Publisher
- Springer-Verlag
- Year
- 1984
- Tongue
- French
- Weight
- 898 KB
- Volume
- 187
- Category
- Article
- ISSN
- 0025-5874
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📜 SIMILAR VOLUMES
Let H be a Hopf algebra with bijective antipode over a commutative ring k. A right H-Galois extension of k is a right H-comodule algebra A such that k s A co H and a certain canonical map A m A ª A m H is a bijection. We investigate Galois connections for Hopf᎐Galois extensions that can be formulate
For H an infinite dimensional co-Frobenius Hopf algebra over a field k, and A an H-comodule algebra, the smash product A࠻H \* r at is linked to the ring of coinvariants A c o H by a Morita context. We use the Morita setting to show that for co-Frobenius H, equivalent conditions for ArA c o H to be G
We prove a Maschke type theorem for Doi᎐Hopf modules. A sufficient condition in order to have a Maschke type property is that there exists a normalized integral map for the Doi᎐Hopf datum in question. The results are applied to graded modules and to Yetter᎐Drinfel'd modules. As another application,