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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On conjugation invariants in the dual Steenrod algebra


Authors: M. D. Crossley and Sarah Whitehouse
Journal: Proc. Amer. Math. Soc. 128 (2000), 2809-2818
MSC (1991): Primary 55S10, 20J06, 20C30
Published electronically: February 29, 2000
MathSciNet review: 1657790
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the canonical conjugation, $\chi $, of the mod $2$ dual Steenrod algebra, $\mathcal{A}_{*}$, with a view to determining the subspace, $\mathcal{A}_{*}^{\chi }$, of elements invariant under $\chi $. We give bounds on the dimension of this subspace for each degree and show that, after inverting $\xi _{1}$, it becomes polynomial on a natural set of generators. Finally we note that, without inverting $\xi _{1}$, $\mathcal{A}_{*}^{\chi }$ is far from being polynomial.


References [Enhancements On Off] (What's this?)

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Additional Information

M. D. Crossley
Affiliation: Max-Planck-Institut für Mathematik, P.O. Box 7280, D-53072 Bonn, Germany
Email: crossley@member.ams.org

Sarah Whitehouse
Affiliation: Département de Mathématiques, Université d’Artois - Pole de Lens, Rue Jean Souvraz, S. P. 18 - 63207 Lens, France
Email: whitehouse@poincare.univ-artois.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05283-7
PII: S 0002-9939(00)05283-7
Received by editor(s): June 19, 1998
Received by editor(s) in revised form: October 19, 1998
Published electronically: February 29, 2000
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society