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    Primitive elements of $\mathbb{Z}_p[x]$

    E-HAT-3.C-7

    Area
    Topology
    Topics
    Cohomology, H-Spaces, Hopf Algebras
    Status
    draft

    What are the primitive elements of the Hopf algebra \(\mathbb{Z}_p[x]\) for \(p\) prime?

    Solution

    1. \(H_*(T^n)\cong\Lambda[x_1,\dots,x_n]\) exterior.

    Kunneth.

    2. Pontryagin product corresponds to algebra structure.

    group law.

    3. Q.E.D.

    2.

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