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Small subalgebras of Steenrod and Morava stabilizer algebras

Authors:	N Yagita

Institution:	Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan

Abstract:	Let (resp. $S(n)_{(j)})$ be the subalgebra of the Steenrod algebra $\mathcal{A}_p$ (resp. th Morava stabilizer algebra) generated by reduced powers $\mathcal{P}^{p^i}$ , $0\le i\le j$ (resp. , $1\le i\le j)$ . In this paper we identify the dual of (resp. $S(n)_{(j)}$ , for $j\le n)$ with some Frobenius kernel (resp. $F_{p^n}$ -points) of a unipotent subgroup 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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