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On the spectral sequence constructors of Guichardet and Stefan

Author(s): Donald W. Barnes
Journal: Trans. Amer. Math. Soc. 355 (2003), 2755-2769.
MSC (2000): Primary 18G40, 16W30; Secondary 16E40
Posted: February 25, 2003
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Abstract: The concept of a spectral sequence constructor is generalised to Hopf Galois extensions. The spectral sequence constructions that are given by Guichardet for crossed product algebras are also generalised and shown to provide examples. It is shown that all spectral sequence constructors for Hopf Galois extensions construct the same spectral sequence.

References:

[1]
D. W. Barnes, Spectral sequence constructors in algebra and topology, Mem. Amer. Math. Soc. 53 (1985). MR 86e:55032

[2]
H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, 1956. MR 17:1040e

[3]
A. Guichardet, Suites spectrales à la Hochschild-Serre pour les produits croisés d'algèbres et de groupes, J. Algebra 235 (2001), 744-765. MR 2001m:16013

[4]
H. J. Schneider, Representation theory of Hopf Galois extensions. Hopf algebras, Israel J. Math. 72 (1990), 196-231. MR 92d:16047

[5]
D. Stefan, Hochschild cohomology on Hopf Galois extensions, J. Pure Appl. Algebra 103 (1995), 221-233. MR 96h:16013

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Additional Information:

Donald W. Barnes
Affiliation: 1 Little Wonga Road, Cremorne NSW 2090, Australia
Email: donb@netspace.net.au

DOI: 10.1090/S0002-9947-03-03270-7
PII: S 0002-9947(03)03270-7
Keywords: Spectral sequence, crossed product, comodule algebra, Hopf Galois extension
Received by editor(s): April 30, 2001
Posted: February 25, 2003
Additional Notes: This work was done while the author was an Honorary Associate of the School of Mathematics and Statistics, University of Sydney
Copyright of article: Copyright 2003, American Mathematical Society

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