Small subalgebras of Steenrod and Morava stabilizer algebras
Author:
N. Yagita
Journal:
Trans. Amer. Math. Soc. 350 (1998), 30213041
MSC (1991):
Primary 55N22; Secondary 57R77
MathSciNet review:
1475699
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Abstract 
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Abstract: Let (resp. be the subalgebra of the Steenrod algebra (resp. th Morava stabilizer algebra) generated by reduced powers , (resp. , . In this paper we identify the dual of (resp. , for with some Frobenius kernel (resp. points) of a unipotent subgroup of the general linear algebraic group . Using these facts, we get the additive structure of for odd primes.
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 [GSS]
 V. Gorbounov, S. Siegel, and P. Symonds, The cohomology of the Morava stabilizer group at the prime , Preprint 1994.
 [KSTY 1]
 M. Kaneda, N. Shimada, M. Tezuka, and N. Yagita, Cohomology of infinitesimal algebraic groups, Math. Z. 205 (1990), 6195. MR 91k:20048
 [KSTY 2]
 , Representations of the Steenrod algebra, J. Algebra 155 (1993), 435453. MR 94b:55025
 [H]
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 [MW]
 H. Miller and C. Wilkerson, Vanishing lines for modules over the Steenrod algebra, J. Pure Appl. Algebra 22 (1981), 293307. MR 82m:55024
 [L 1]
 I. Leary, The cohomology of certain finite groups, Thesis, Cambridge Univ., 1990.
 [L 2]
 , A differential in the LyndonHochschildSerre spectral sequence, J. Pure Appl. Algebra 88 (1993), 155168. MR 94m:20102
 [Li]
 A. Liulevicius, The factorization of cyclic reduced power by secondary cohomology operation, Mem. Amer. Math. Soc. 42, 1962. MR 31:6226
 [PY]
 C. Peterson and N. Yagita, Rational cohomology of Witt groups, Math. Z. 224 (1997), 665676. CMP 97:13
 [Q]
 D. Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. 94 (1971), 549572; 573602. MR 45:7743
 [R 1]
 D. Ravenel, The structure of Morava stabilizer algebras, Invent. Math. 37 (1976), 109120. MR 54:8632
 [R 2]
 , The cohomology of the Morava stabilizer algebra, Math. Z. 152 (1977), 287297. MR 55:4170
 [R 3]
 , Complex cobordism and stable homotopy groups of spheres, Academic Press, New York, 1986. MR 87j:55003
 [SI]
 N. Shimada and A. Iwai, On the cohomology of some Hopf algebras, Nagoya Math. J. 30 (1967), 103111. MR 35:6731
 [T]
 M. Tezuka, Cohomology of unipotent algebraic and finite groups and the Steenrod algebra, Math. Z. 216 (1994), 4567. MR 95c:20064
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 N. Yagita, Frobenius operations and cohomology of , Comm. Algebra 16 (1988), 9891016. MR 89c:20077
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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/S0002994798022260
PII:
S 00029947(98)022260
Received by editor(s):
January 9, 1995
Article copyright:
© Copyright 1998
American Mathematical Society
