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The smallest subgroup whose invariants are hit by the Steenrod algebra

Published online by Cambridge University Press:  12 February 2007

NGUYỄN H. V. HƯNG  and
TRAN DINH LUONG
NGUYỄN H. V. HƯNG
Affiliation:
Department of Mathematics, Vietnam National University, Hanoi 334 Nguyễn Trãi Street, Hanoi, Vietnam. e-mail: nhvhung@vnu.edu.vn
TRAN DINH LUONG
Affiliation:
Department of Mathematics, Quynhon University, 170 An Duong Vuong Street, Quynhon, Vietnam. e-mail: tdinhluong@yahoo.com
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Abstract

Let V be a k-dimensional -vector space and let W be an n-dimensional vector subspace of V. Denote by GL(n, ) • 1 k-n the subgroup of GL(V) consisting of all isomorphisms ϕ:V → V with ϕ(W) = W and ϕ(v) ≡ v (mod W) for every v ∈ V. We show that GL(3, ) • 1 k-3 is, in some sense, the smallest subgroup of GL(V)≅ GL(k, , whose invariants are hit by the Steenrod algebra acting on the polynomial algebra, . The result is some aspect of an algebraic version of the classical conjecture that the only spherical classes inQ 0 S 0are the elements of Hopf invariant one and those of Kervaire invariant one.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 63 - 71
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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