A Hopf algebra having a separable Galois extension is finite dimensional
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Abstract:
It is shown that a Hopf algebra $H$ over a field admitting a Galois extension $A$ separable over its subalgebra of coinvariants $B$ is of finite dimension. This answers in the affirmative a question posed by Beattie et al. in [Proc. Amer. Math. Soc. 128, No. 11 (2000), 3201-3203]. It is also proven that this result holds true if $H$ has bijective antipode and the extension $A/B$ is Frobenius.References
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Additional Information
- Juan Cuadra
- Affiliation: Universidad de Almería, Depto. Álgebra y Análisis Matemático, E-04120 Almería, Spain
- Email: jcdiaz@ual.es
- Received by editor(s): January 17, 2007
- Received by editor(s) in revised form: March 1, 2007, and March 13, 2007
- Published electronically: May 29, 2008
- Additional Notes: This research was supported by projects MTM2005-03227 from MCYT and FEDER and P06-FQM-1889 from Junta de Andalucía
- Communicated by: Birge Huisgen-Zimmermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3405-3408
- MSC (2000): Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9939-08-09557-9
- MathSciNet review: 2415022
Dedicated: To José Luis Gómez Pardo on the occasion of his 60th birthday