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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Small subalgebras of Steenrod and
Morava stabilizer algebras


Author: N. Yagita
Journal: Trans. Amer. Math. Soc. 350 (1998), 3021-3041
MSC (1991): Primary 55N22; Secondary 57R77
MathSciNet review: 1475699
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Abstract: Let $P(j)$ (resp. $S(n)_{(j)})$ be the subalgebra of the Steenrod algebra $\mathcal{A}_p$ (resp. $n$th Morava stabilizer algebra) generated by reduced powers $\mathcal{P}^{p^i}$, $0\le i\le j$ (resp. $t_i$, $1\le i\le j)$. In this paper we identify the dual $P(j-1)^*$ of $P(j-1)$ (resp. $S(n)_{(j)}$, for $j\le n)$ with some Frobenius kernel (resp. $F_{p^n}$-points) of a unipotent subgroup $G(j+1)$ of the general linear algebraic group $GL_{j+1}$. Using these facts, we get the additive structure of $H^*(P(1))=\operatorname{Ext}_{P(1)}(Z/p,Z/p)$ for odd primes.


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Additional Information

N. Yagita
Affiliation: Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
Email: yagita@mito.ipc.ibaraki.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02226-0
PII: S 0002-9947(98)02226-0
Received by editor(s): January 9, 1995
Article copyright: © Copyright 1998 American Mathematical Society