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November 2009 On the cohomology of the mod p Steenrod algebra
Xiugui Liu, He Wang
Proc. Japan Acad. Ser. A Math. Sci. 85(9): 143-148 (November 2009). DOI: 10.3792/pjaa.85.143

Abstract

Let p be an odd prime greater than seven and A the mod p Steenrod algebra. In this paper we prove that in the cohomology of A the product $h_1 h_n \tilde \delta _{s + 4}\in {\rm Ext}_A^{s + 6, t(s,n) + s} ({\bf Z}_p , {\bf Z}_p)$ is nontrivial for $n \geq 5$, and trivial for $n=3, 4$, where $ \tilde \delta _{s + 4}$ is actually $\tilde \alpha _{s+4}^{(4)}$ described by X. Wang and Q. Zheng, $0 \leq s < p - 4$, $t(s,n) = 2(p-1)[(s + 1) + (s + 3)p + (s + 3)p^2 + (s + 4)p^3 + p^n ].$ We show our results by explicit combinatorial analysis of the (modified) May spectral sequence. The method of proof is very elementary.

Citation

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Xiugui Liu. He Wang. "On the cohomology of the mod p Steenrod algebra." Proc. Japan Acad. Ser. A Math. Sci. 85 (9) 143 - 148, November 2009. https://doi.org/10.3792/pjaa.85.143

Information

Published: November 2009
First available in Project Euclid: 5 November 2009

zbMATH: 1186.55008
MathSciNet: MR2573964
Digital Object Identifier: 10.3792/pjaa.85.143

Subjects:
Primary: 55S10
Secondary: 55T15

Keywords: Adams spectral sequence , Cohomology , May spectral sequence , Steenrod algebra

Rights: Copyright © 2009 The Japan Academy

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Vol.85 • No. 9 • November 2009
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