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A bialgebra that admits a Hopf-Galois extension is a Hopf algebra
Author(s):
Peter
Schauenburg
Journal:
Proc. Amer. Math. Soc.
125
(1997),
83-85.
MSC (1991):
Primary 16W30
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Abstract:
Let  be a commutative ring. Assume that  is a  -bialgebra, and  is an  -Galois extension of its coinvariant subalgebra  . Provided  is faithfully flat over  , we show that  is necessarily a Hopf algebra.
References:
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- DOI, Y., AND TAKEUCHI, M. Cleft comodule algebras for a bialgebra. Comm. in Alg. 14 (1986), 801-817. MR 87e:16025
- 2.
- DOI, Y., AND TAKEUCHI, M. Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras. J. Algebra 121 (1989), 488-516. MR 90b:16015
- 3.
- MONTGOMERY, S. Hopf algebras and their actions on rings, vol. 82 of CBMS Regional Conference Series in Mathematics. AMS, Providence, Rhode Island, 1993. MR 94i:16019
- 4.
- SCHAUENBURG, P. Hopf bimodules over Hopf-Galois extensions, Miyashita-Ulbrich actions, and monoidal center constructions. Comm. in Alg. 24 (1996), 143-163.
- 5.
- SCHNEIDER, H.-J. Representation theory of Hopf-Galois extensions. Israel. J. of Math. 72 (1990), 196-231. MR 92d:16047
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Additional Information:
Peter
Schauenburg
Affiliation:
Department of Mathematics University of Southern California, Los Angeles, California 90089
Address at time of publication:
Mathematisches Institut der Universität München Theresienstr. 39 80333 München Germany
Email:
schauen@rz.mathematik.uni-muenchen.de
DOI:
10.1090/S0002-9939-97-03682-4
PII:
S 0002-9939(97)03682-4
Received by editor(s):
April 26, 1995
Received by editor(s) in revised form:
August 4, 1995
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1997,
American Mathematical Society
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