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On the Projectivity of module coalgebras

Author: Siu-Hung Ng
Journal: Proc. Amer. Math. Soc. 126 (1998), 3191-3198
MSC (1991): Primary 16W30
MathSciNet review: 1469428
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Abstract: In this paper, we derive some criteria for the projectivity of a module coalgebra over a finite dimensional Hopf algebra. In particular, we show that any Hopf algebra over a field of characteristic zero is faithfully flat over its group-like subHopf algebra. Finally, we prove that if $B$ is a finite dimensional subHopf algebra of a Hopf algebra $A$, then $B$ is normal in $A$ if and only if $AB^+ = B^+\!A$. This improves a result by S. Montgomery (1993).

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Additional Information

Siu-Hung Ng
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication: Department of Mathematics, University of California at Santa Cruz, Santa Cruz, California 95064

Received by editor(s): September 27, 1996
Received by editor(s) in revised form: April 3, 1997
Communicated by: Ken Goodearl
Article copyright: © Copyright 1998 American Mathematical Society