Primitively generated Hopf orders in characteristic $p$

Alan Koch

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arXiv · 1509.07393

Primitively generated Hopf orders in characteristic $p$

Alan Koch

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Abstract

Let $R$ be a characteristic $p$ discrete valuation ring with field of fractions $K$. Let $H$ be a commutative, cocommutative $K$-Hopf algebra of $p$-power rank which is generated as a $K$-algebra by primitive elements. We construct all of the $R$-Hopf orders of $H$ in $K$; each Hopf order corresponds to a solution to a single matrix equation. For $R$ complete, we give explicit examples of Hopf orders in some rank $p^2$ $K$-Hopf algebras.

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Alan Koch. 2015-09-24. Primitively generated Hopf orders in characteristic $p$. https://arxiv.org/abs/1509.07393

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