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A Hopf algebra having a separable Galois extension is finite dimensional
Author(s):
Juan
Cuadra
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3405-3408.
MSC (2000):
Primary 16W30
Posted:
May 29, 2008
MathSciNet review:
2415022
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Abstract:
It is shown that a Hopf algebra  over a field admitting a Galois extension  separable over its subalgebra of coinvariants  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  has bijective antipode and the extension  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
DOI:
10.1090/S0002-9939-08-09557-9
PII:
S 0002-9939(08)09557-9
Received by editor(s):
January 17, 2007,
Received by editor(s) in revised form:
March 1, 2007, and March 13, 2007
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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