On conjugation invariants in the dual Steenrod algebra
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- by M. D. Crossley and Sarah Whitehouse PDF
- Proc. Amer. Math. Soc. 128 (2000), 2809-2818 Request permission
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
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2809-2818
- MSC (1991): Primary 55S10, 20J06, 20C30
- DOI: https://doi.org/10.1090/S0002-9939-00-05283-7
- MathSciNet review: 1657790