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Projective and Injective Hopf Algebras Over the Dyer-Lashof Algebra

Published online by Cambridge University Press:  20 November 2018

Paul G. Goerss
Paul G. Goerss*
Affiliation:
Department of Mathematics University of Washington Seattle, Washington 98195 U.S.A
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Abstract

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The purpose of this paper is to discuss the existence, structure, and properties of certain projective and injective Hopf algebras in the category of Hopf algebras that support the structure one expects on the homology of an infinite loop space. As an auxiliary project, we show that these projective and injective Hopf algebras can be realized as the homology of infinite loop spaces associated to spectra obtained from Brown-Gitler spectra by Spanier-Whitehead duality and Brown-Comenetz duality, respectively. We concentrate mainly on indecomposable projectives and injectives, and we work only at the prime 2.

Keywords

55P3555N99Hopf algebrasDyer-Lashof algebraprojective and injective objectsBrown-Gitler spectra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 944 - 976
Copyright
Copyright © Canadian Mathematical Society 1993

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