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A co-Frobenius Hopf algebra with a separable Galois extension is finite

Author(s): M. Beattie; S. Dascalescu; S. Raianu
Journal: Proc. Amer. Math. Soc. 128 (2000), 3201-3203.
MSC (1991): Primary 16W30
Posted: May 18, 2000
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Abstract:

If $H$ is a co-Frobenius Hopf algebra over a field, having a Galois $H$-object $A$which is separable over $A^{coH}$, its ring of coinvariants, then $H$ is finite dimensional.

References:

1.
M. Beattie, S. Dascalescu and S. Raianu, Galois extensions for co-Frobenius Hopf algebras, J. Algebra 198 (1997), 164-183. MR 99c:16034

2.
M. Beattie, S. Dascalescu, L. Grünenfelder and C. Nastasescu, Finiteness conditions, co-Frobenius Hopf algebras and quantum groups, J. Algebra 200 (1998), 312-333. MR 99c:16035

3.
M. Cohen and D. Fischman, Semisimple extensions and elements of trace 1, J. Algebra 149 (1992), 419-437. MR 93c:16038

4.
B. Lin, Semiperfect coalgebras, J. Alg. 49 (1977), 357-373. MR 58:16749

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Additional Information:

M. Beattie
Affiliation: Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada E4L 1E6
Email: mbeattie@mta.ca

S. Dascalescu
Affiliation: University of Bucharest, Faculty of Mathematics, Str. Academiei 14, RO-70109 Bucharest 1, Romania
Email: sdascal@al.math.unibuc.ro

S. Raianu
Affiliation: University of Bucharest, Faculty of Mathematics, Str. Academiei 14, RO-70109 Bucharest 1, Romania
Email: sraianu@al.math.unibuc.ro

DOI: 10.1090/S0002-9939-00-05437-X
PII: S 0002-9939(00)05437-X
Received by editor(s): August 12, 1998
Received by editor(s) in revised form: January 15, 1999
Posted: May 18, 2000
Additional Notes: The first author's research was partially supported by NSERC
The last two authors thank Mount Allison University for their kind hospitality.
Communicated by: Ken Goodearl
Copyright of article: Copyright 2000, American Mathematical Society

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