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A Hopf algebra having a separable Galois extension is finite dimensional

Author: Juan Cuadra
Journal: Proc. Amer. Math. Soc. 136 (2008), 3405-3408
MSC (2000): Primary 16W30
Published electronically: May 29, 2008
MathSciNet review: 2415022
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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.

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Additional Information

Juan Cuadra
Affiliation: Universidad de Almería, Depto. Álgebra y Análisis Matemático, E-04120 Almería, Spain

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
Dedicated: To José Luis Gómez Pardo on the occasion of his 60th birthday
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.