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| Titel: |
A note on frobenius extensions in hopf algebras |
| Auteur: |
Doi, Yukio |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 25 (1997) nr. 11 pagina's 3699-3710 |
| Jaar: |
1997 |
| Inhoud: |
Let H be a Hopf algebra over a field with bijective antipode and K a Hopf subalgebra with K =coπ(H)(H), where π(H)= H/HK+.Using Miyashita-Ulbrich type action on Endl-H-K(H), we show (Cor of Thm 2) that the extension K ⊂H is of right integral type in the sense of [FMS] if and only if it is β-Frobenius such that both βand the β-Frobenius map are H-colinear. We also improve some results in [FMS]. Throughout H denotes a Hopf algebra over a field k with comultiplication △, counit εand antipode S. Let B ⊂A be an extension of right H-comodule algebras, that is, A is a right H-comodule algebra with structure map ρA and B is a subalgebra with ρA(B) ⊂ B⊗H In this note we consider when B ⊂A is a β-Frobenius extension such that both βand the corresponding β-Frobenius map are H-colinear. Following [T] we call such an extension a β-H-Frobenius extension, we follow Fischman-Montgomery-Schneider's paper [FMS] for the terminology on β-Frobenius extensions, extensions of right integral type, etc. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 3 van 20 gevonden artikelen
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