Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the cohomology of the mod p Steenrod algebra

Xiugui Liu and He Wang

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 85, Number 9 (2009), 143-148.

First available in Project Euclid: 5 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S10: Steenrod algebra
Secondary: 55T15: Adams spectral sequences

Steenrod algebra cohomology Adams spectral sequence May spectral sequence


Liu, Xiugui; Wang, He. On the cohomology of the mod p Steenrod algebra. Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 9, 143--148. doi:10.3792/pjaa.85.143.

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