Hopf orders in $K[C_p^3]$ in characteristic $p$

Let $p$ be prime, let $K$ be a non-archimedean local field of characteristic $p$ and let $C_{p}^{3}$ denote the elementary abelian group of order $p^{3}$ . We give a complete classification of Hopf orders in the $K$ -Hopf algebra $(K [C_{p}^{3}])^{*}$ and under a mild condition compute their dual Hopf orders in the group ring $K [C_{p}^{3}]$ .

Hopf orders in $K [C_{p}^{3}]$ in characteristic $p$

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Hopf orders in $K [C_{p}^{3}]$ in characteristic $p$

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Hopf orders in K[Cp3]K[Cp3​] in characteristic pp

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Hopf orders in K[Cp3]K[Cp3​] in characteristic pp

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Hopf orders in $K [C_{p}^{3}]$ in characteristic $p$

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Hopf orders in $K [C_{p}^{3}]$ in characteristic $p$

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