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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Small subalgebras of Steenrod and Morava stabilizer algebras
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by N. Yagita PDF
Trans. Amer. Math. Soc. 350 (1998), 3021-3041 Request permission

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.
References
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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
  • © Copyright 1998 American Mathematical Society
  • 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