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

DOI:
https://doi.org/10.1090/S0002-9947-98-02226-0

MathSciNet review:
1475699

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Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
185110

Email:
yagita@mito.ipc.ibaraki.ac.jp

Received by editor(s):
January 9, 1995

Article copyright:
© Copyright 1998
American Mathematical Society