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On the Semi-Tensor Product of the Dyer-Lashof and Steenrod Algebras

Published online by Cambridge University Press:  20 November 2018

H. E. A. Campbell  and
P. S. Selick
H. E. A. Campbell
Affiliation:
Queen's University, Kingston, Ontario
P. S. Selick
Affiliation:
University of Toronto, Toronto, Ontario
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This paper arises out of joint work with F. R. Cohen and F. P. Peterson [5, 2, 3] on the joint structure of infinite loop spaces QX. The homology of such a space is operated on by both the Dyer-Lashof algebra, R, and the opposite of the Steenrod algebra A∗. We describe a convenient summary of these actions; let M be the algebra which is R ⊗ A∗ as a vector space and where multiplication Q1 ⊗ PJ. Q1’ ⊗ PJ’∗ is given by applying the Nishida relations in the middle and then the appropriate Adem relations on the ends. Then M is a Hopf algebra which acts on the homology of infinite loop spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 4 , 01 August 1989 , pp. 676 - 701
Copyright
Copyright © Canadian Mathematical Society 1989

References

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