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On the mod p Steenrod algebra and the Leibniz-Hopf algebra

  • Received: 01 March 2020 Revised: 01 May 2020
  • Primary: 55S10, 16T05; Secondary: 57T05

  • Let $ p $ be a fixed odd prime. The Bockstein free part of the mod $ p $ Steenrod algebra, $ \mathcal{A}_p $, can be defined as the quotient of the mod $ p $ reduction of the Leibniz Hopf algebra, $ \mathcal{F}_p $. We study the Hopf algebra epimorphism $ \pi\colon \mathcal{F}_p\to \mathcal{A}_p $ to investigate the canonical Hopf algebra conjugation in $ \mathcal{A}_p $ together with the conjugation operation in $ \mathcal{F}_p $. We also give a result about conjugation invariants in the mod 2 dual Leibniz Hopf algebra using its multiplicative algebra structure.

    Citation: Neşet Deniz Turgay. On the mod p Steenrod algebra and the Leibniz-Hopf algebra[J]. Electronic Research Archive, 2020, 28(2): 951-959. doi: 10.3934/era.2020050

    Related Papers:

  • Let $ p $ be a fixed odd prime. The Bockstein free part of the mod $ p $ Steenrod algebra, $ \mathcal{A}_p $, can be defined as the quotient of the mod $ p $ reduction of the Leibniz Hopf algebra, $ \mathcal{F}_p $. We study the Hopf algebra epimorphism $ \pi\colon \mathcal{F}_p\to \mathcal{A}_p $ to investigate the canonical Hopf algebra conjugation in $ \mathcal{A}_p $ together with the conjugation operation in $ \mathcal{F}_p $. We also give a result about conjugation invariants in the mod 2 dual Leibniz Hopf algebra using its multiplicative algebra structure.



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