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

MathSciNet review:
1475699

Full-text PDF Free Access

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]**Leonard Evens,*The cohomology of groups*, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR**1144017****[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]**Masaharu Kaneda, Nobuo Shimada, Michishige Tezuka, and Nobuaki Yagita,*Cohomology of infinitesimal algebraic groups*, Math. Z.**205**(1990), no. 1, 61–95. MR**1069485**, 10.1007/BF02571225**[K-S-T-Y 2]**Masaharu Kaneda, Nobuo Shimada, Michishige Tezuka, and Nobuaki Yagita,*Representations of the Steenrod algebra*, J. Algebra**155**(1993), no. 2, 435–454. MR**1212238**, 10.1006/jabr.1993.1053**[H]**H-W. Henn,*On the cohomology of profinite groups of positive rank*, Preprint, 1994.**[M-W]**Haynes Miller and Clarence Wilkerson,*Vanishing lines for modules over the Steenrod algebra*, J. Pure Appl. Algebra**22**(1981), no. 3, 293–307. MR**629336**, 10.1016/0022-4049(81)90104-3**[L 1]**I. Leary,*The cohomology of certain finite groups*, Thesis, Cambridge Univ., 1990.**[L 2]**Ian Leary,*A differential in the Lyndon-Hochschild-Serre spectral sequence*, J. Pure Appl. Algebra**88**(1993), no. 1-3, 155–168. MR**1233320**, 10.1016/0022-4049(93)90019-P**[Li]**Arunas Liulevicius,*The factorization of cyclic reduced powers by secondary cohomology operations*, Mem. Amer. Math. Soc. No.**42**(1962), 112. MR**0182001****[P-Y]**C. Peterson and N. Yagita,*Rational cohomology of Witt groups*, Math. Z.**224**(1997), 665-676. CMP**97:13****[Q]**Daniel Quillen,*The spectrum of an equivariant cohomology ring. I, II*, Ann. of Math. (2)**94**(1971), 549–572; ibid. (2) 94 (1971), 573–602. MR**0298694****[R 1]**Douglas C. Ravenel,*The structure of Morava stabilizer algebras*, Invent. Math.**37**(1976), no. 2, 109–120. MR**0420619****[R 2]**Douglas C. Ravenel,*The cohomology of the Morava stabilizer algebras*, Math. Z.**152**(1977), no. 3, 287–297. MR**0431168****[R 3]**Douglas C. Ravenel,*Complex cobordism and stable homotopy groups of spheres*, Pure and Applied Mathematics, vol. 121, Academic Press, Inc., Orlando, FL, 1986. MR**860042****[S-I]**Nobuo Shimada and Akira Iwai,*On the cohomology of some Hopf algebras*, Nagoya Math. J.**30**(1967), 103–111. MR**0215896****[T]**Michishige Tezuka,*Cohomology of unipotent algebraic and finite groups and the Steenrod algebra*, Math. Z.**216**(1994), no. 1, 45–67. MR**1273465**, 10.1007/BF02572308**[Y]**Nobuaki Yagita,*Frobenius operations and cohomology of 𝐺𝐿₃(𝐹_{𝑞})*, Comm. Algebra**16**(1988), no. 5, 989–1016. MR**926333**, 10.1080/00927878808823614

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
55N22,
57R77

Retrieve articles in all journals with MSC (1991): 55N22, 57R77

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/S0002-9947-98-02226-0

Received by editor(s):
January 9, 1995

Article copyright:
© Copyright 1998
American Mathematical Society