Journal of Homotopy and Related Structures

, Volume 12, Issue 3, pp 727–739 | Cite as

The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra

  • Neşet Deniz Turgay
  • Shizuo Kaji


The mod 2 Steenrod algebra \(\mathcal {A}_2\) can be defined as the quotient of the mod 2 Leibniz–Hopf algebra \(\mathcal {F}_2\) by the Adem relations. Dually, the mod 2 dual Steenrod algebra \(\mathcal {A}_2^*\) can be thought of as a sub-Hopf algebra of the mod 2 dual Leibniz–Hopf algebra \(\mathcal {F}_2^*\). We study \(\mathcal {A}_2^*\) and \(\mathcal {F}_2^*\) from this viewpoint and give generalisations of some classical results in the literature.


Leibniz–Hopf algebra Steenrod algebra Adem relation Hopf algebra Conjugation Antipode 

Mathematics Subject Classification

55S10 16T05 57T05 



We would like to thank Stephen Theriault, Martin Crossley, and Carmen Rovi for their comments on the earlier version of this paper.


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Copyright information

© Tbilisi Centre for Mathematical Sciences 2016

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Arts and Sciences, Eastern Mediterranean UniversityGazimagusaTurkey
  2. 2.Department of Mathematical Sciences, Faculty of ScienceYamaguchi UniversityYamaguchiJapan

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