### Electronic Research Archive

2020, Issue 2: 951-959. doi: 10.3934/era.2020050
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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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