Primitively generated Hopf orders in characteristic p

2015/09/24 by Alan Koch, Koch, Alan
Mathematics · #14L15 #16T05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras #math.NT #msc:14L15 #msc:16T05

paper · pdf · doi:10.48550/arxiv.1509.07393

17 pages

arxiv created 2015/09/24 · openalex publication_date 2015/09/24 · arxiv updated 2015/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 p² K-Hopf algebras.

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