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A bialgebra that admits a Hopf-Galois extension is a Hopf algebra

Author: Peter Schauenburg
Journal: Proc. Amer. Math. Soc. 125 (1997), 83-85
MSC (1991): Primary 16W30
MathSciNet review: 1363183
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Abstract: Let $k$ be a commutative ring. Assume that $H$ is a $k$-bialgebra, and $A$ is an $H$-Galois extension of its coinvariant subalgebra $B$. Provided $A$ is faithfully flat over $k$, we show that $H$ is necessarily a Hopf algebra.

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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

Received by editor(s): April 26, 1995
Received by editor(s) in revised form: August 4, 1995
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society

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