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 (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.

**[E]**L. Evens,*Cohomology of groups*, Oxford Univ. Press, 1991. MR**93i:20059****[G-S-S]**V. Gorbounov, S. Siegel, and P. Symonds,*The cohomology of the Morava stabilizer group at the prime*, Preprint 1994.**[K-S-T-Y 1]**M. Kaneda, N. Shimada, M. Tezuka, and N. Yagita,*Cohomology of infinitesimal algebraic groups*, Math. Z.**205**(1990), 61-95. MR**91k:20048****[K-S-T-Y 2]**-,*Representations of the Steenrod algebra*, J. Algebra**155**(1993), 435-453. MR**94b:55025****[H]**H-W. Henn,*On the cohomology of profinite groups of positive rank*, Preprint, 1994.**[M-W]**H. Miller and C. Wilkerson,*Vanishing lines for modules over the Steenrod algebra*, J. Pure Appl. Algebra**22**(1981), 293-307. MR**82m:55024****[L 1]**I. Leary,*The cohomology of certain finite groups*, Thesis, Cambridge Univ., 1990.**[L 2]**-,*A differential in the Lyndon-Hochschild-Serre spectral sequence*, J. Pure Appl. Algebra**88**(1993), 155-168. 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****[P-Y]**C. Peterson and N. Yagita,*Rational cohomology of Witt groups*, Math. Z.**224**(1997), 665-676. CMP**97:13****[Q]**D. Quillen,*The spectrum of an equivariant cohomology ring*. I, II, Ann. of Math.**94**(1971), 549-572; 573-602. MR**45:7743****[R 1]**D. Ravenel,*The structure of Morava stabilizer algebras*, Invent. Math.**37**(1976), 109-120. MR**54:8632****[R 2]**-,*The cohomology of the Morava stabilizer algebra*, Math. Z.**152**(1977), 287-297. MR**55:4170****[R 3]**-,*Complex cobordism and stable homotopy groups of spheres*, Academic Press, New York, 1986. MR**87j:55003****[S-I]**N. Shimada and A. Iwai,*On the cohomology of some Hopf algebras*, Nagoya Math. J.**30**(1967), 103-111. MR**35:6731****[T]**M. Tezuka,*Cohomology of unipotent algebraic and finite groups and the Steenrod algebra*, Math. Z.**216**(1994), 45-67. MR**95c:20064****[Y]**N. Yagita,*Frobenius operations and cohomology of*, Comm. Algebra**16**(1988), 989-1016. 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:
https://doi.org/10.1090/S0002-9947-98-02226-0

Received by editor(s):
January 9, 1995

Article copyright:
© Copyright 1998
American Mathematical Society