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Etude de la categorie des algebres de Hopf commutatives connexes sur un corps

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Abstract

Let k be a perfect field of characteristic p≠0; the categoryH of connected abelian Hopf algebras over k is abelian and locally noetherian. Technics of locally noetherian categories are used here to obtain Krull and homological dimensions ofH (which are respectively 1 and 2), and a decomposition ofH in a product of categories. First we have

, whereH is the category of Grassman algebras, andH + consists of Hopf algebras which are zero in odd degrees; then we prove thatH + itself is a product of isomorphic categoriesH n, n∈ℕ*, and we give an equivalence betweenH n and a category of modules. This is compared to some results of algebraic geometry about Greenberg modules.

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Schoeller, C. Etude de la categorie des algebres de Hopf commutatives connexes sur un corps. Manuscripta Math 3, 133–155 (1970). https://doi.org/10.1007/BF01273307

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  • DOI: https://doi.org/10.1007/BF01273307

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