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.
Similar content being viewed by others
Bibliographie
FREYD P.: Abelian categories, Harper International Editions, (1966).
GABRIEL P.: Séminaire J.P. Serre (1960).
GABRIEL P.: Des catégories abéliennes, Bull. Soc. Math. France 90, 323–448 (1962).
GABRIEL P. et DEMAZURE M.: Groupes algébriques linéaires, North Holland Publishing Company (à paraître).
MILNOR J. and MOORE J.C.: On the structure of Hopf algebras, Ann. Math. 81, 211–264 (1965).
MILNOR J. and MOORE J.C.: On the structure of Hopf Algebras, Princeton, multigraphié (1960).
WRAITH G.C.: Abelian Hopf algebras, J. Algebra 6, 135–156 (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01273307