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Let $E^r$ be a commutative Hopf algebra homology spectral sequence over $\mathbb{Z}/p$, i.e. such that every sheet is a commutative Hopf algebra.

I am struggling with proving (probably simple) fact - that every transgressive element in such a spectral sequence is primitive.

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    $\begingroup$ How do the differentials interact with the Hopf algebra structure? $\endgroup$
    – Denis Nardin
    Commented Mar 5, 2019 at 21:44
  • $\begingroup$ They are morphisms of Hopf algebras, and are derivations w.r.t. multiplication and the tensor product, as far as I understand. $\endgroup$
    – Igor Sikora
    Commented Mar 6, 2019 at 15:02
  • $\begingroup$ How can they be both morphisms of Hopf algebras and (co?)derivations? $\endgroup$
    – Denis Nardin
    Commented Mar 6, 2019 at 15:32
  • $\begingroup$ Sorry, you are right - a multiplication and comultiplication should be morphisms of spectral sequences. Hopefully it makes sense now $\endgroup$
    – Igor Sikora
    Commented Mar 6, 2019 at 15:44

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