# Operations and co-operations in Morava E-theory

## Mark Hovey

Let $E=E_{n}$ denote the Morava $E$-theory spectrum, and let $\Gamma$ be the Morava stabilizer group of ring spectrum isomorphisms of $E$. We revisit the isomorphism $\pi_{*}L_{K(n)}(E\smash E)\cong C(\Gamma , E_{*})$ of graded formal Hopf algebroids, and its dual isomorphism $E^{*}E\cong E_{*}[[\Gamma]]$.

Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp. 201-236

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