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Invariant theory and Steenrod operations – maps between rings of invariants

Published online by Cambridge University Press:  24 October 2008

Zafer Mahmud  and
Larry Smith
Zafer Mahmud
Affiliation:
Department of Mathematics, University of Kuwait, Kuwait City, Kuwait e-mail: [email protected]
Larry Smith
Affiliation:
Mathematisches Institut der Universität, Bunsenstrasse 3–5, D 37073 Göttingen, Germany e-mail: [email protected]
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Abstract

Let G ′, G ″ be finite groups and p ′: G ↪ GL(n ′,ℚ), p ″: G ″ ↪ GL(n ″, ℚ) faithful rational representations. If T: V′ = ℚn′ → ℚn″ = V ″ is a linear transformation and Ξ: G ′ → G ″ a function such that

then there are induced algebra homomorphisms ℚ[V ″] → ℚ[V ] and ℚ[V ″]G ″ → ℚ[V ′]G ′ making the diagram

commute. In this note we isolate the invariant theory portion of [1] and extend it to provide a necessary and sufficient condition that an algebra homomorphism between rings of invariants ℚ[V ″]G ″ → ℚ[V ′]G ′ arises in this way.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 1 , July 1996 , pp. 103 - 116
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Adams, J. F. and Mahmud, Z.. Maps between classifying spaces. Inventiones Math. 35 (1976), 1–41.CrossRefGoogle Scholar
[2]Lang, S.. Algebraic number theory (Springer-Verlag, 1994).CrossRefGoogle Scholar
[3]Smith, L.. Realizing nonmodular polynomial algebras as the cohomology of spaces of finite type fibered over × BU(d). Pacific J. of Math. 127 (1987), 361–387.CrossRefGoogle Scholar
[4]Smith, L.. Polynomial invariants of finite groups (A. K. Peters Ltd, 1995).CrossRefGoogle Scholar
[5]Smith, L.. -Invariant ideals in rings of invariants. Forum Math., to appear.Google Scholar
[6]Smith, L. and Stong, R. E.. On the invariant theory of finite groups: orbit polynomials and splitting principles. J. Algebra 110 (1987), 134–157.Google Scholar
[7]Weyl, H.. The classical groups, second edition (Princeton University Press, 1946).Google Scholar