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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nonrealizability of subalgebras of $ \mathfrak{A}^*$


Author: Stanley O. Kochman
Journal: Proc. Amer. Math. Soc. 113 (1991), 867-870
MSC: Primary 55P42; Secondary 55N22, 55S10, 55T15
MathSciNet review: 1070521
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Abstract: At the prime two, the dual of the Steenrod algebra is a polynomial algebra in generators $ {\xi _n},n \geq 1$. The Eilenberg-Mac Lane spectrum $ K({Z_2})$ has homology $ {Z_2}[{\xi _n}\vert n \geq 1]$, the Brown-Peterson spectrum BP has homology $ {Z_2}[\xi _n^2\vert n \geq 1]$, and the symplectic Thom spectrum MSp has homology $ {Z_2}[\xi _n^4\vert n \geq 1] \otimes \mathfrak{S}$. In this paper, we show that there is no spectrum $ {B_k}$ with $ {H_*}{B_k} = {Z_2}[\xi _n^{{2^k}}\vert n \geq 1]$ for $ k \geq 2$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1070521-4
Article copyright: © Copyright 1991 American Mathematical Society