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Sub-Hopf-algebras of the Steenrod algebra

Published online by Cambridge University Press:  24 October 2008

J. F. Adams  and
H. R. Margolis
J. F. Adams
Affiliation:
Cambridge University, Cambridge, England
H. R. Margolis
Affiliation:
Boston College, Chestnut Hill, Massachusetts
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Extract

In (3) the second author has shown that all sub-Hopf-algebras of the mod 2 Steenrod algebra have a certain form; this resulthas been used in (1) and (2). The analogous result for the mod p Steenrod algebra, where p is an odd prime, is contained in (6). The object of this paper is to give a shorter proof of a slightly sharper result; we construct all the subalgebras in question. In the mod 2 case this sharper result has also been obtained by Anderson and Davis (2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 45 - 52
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Adams, J. F. and Margolis, H. R.Modules over the Steenrod Algebra, Topology 10 (1971),271–282.CrossRefGoogle Scholar
(2)Anderson, D. W. and Davis, D. M. A Vanishing Theorem in Homological Algebra, to appear.Google Scholar
(3)Margolis, H. R. Coalgebras over the Steenrod Algebra, to appear.Google Scholar
(4)Milnor, J.The Steenrod Algebra and its Dual. Ann. of Math. (2) 67 (1958), 150–171.CrossRefGoogle Scholar
(5)Milnor, J. and Moore, J. C.On the structure of Hopf Algebras. Ann. of Math. (2) 81 (1965), 211–264.CrossRefGoogle Scholar
(6)Rosen, S. S. On Torsion in Connective Complex Cobordism. Thesis, Northwestern University, 1972.Google Scholar