Nilpotence, radicaux et structures mono\\\"{\\i}dales - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Rendiconti del Seminario Matematico della Università di Padova Année : 2002

Nilpotence, radicaux et structures mono\\\"{\\i}dales

Résumé

For $K$ a field, a Wedderburn $K$-linear category is a $K$-linear category $\\sA$ whose radical $\\sR$ is locally nilpotent and such that $\\bar \\sA:=\\sA/\\sR$ is semi-simple and remains so after any extension of scalars. We prove existence and uniqueness results for sections of the projection $\\sA\\to \\bar\\sA$, in the vein of the theorems of Wedderburn. There are two such results: one in the general case and one when $\\sA$ has a monoidal structure for which $\\sR$ is a monoidal ideal. The latter applies notably to Tannakian categories over a field of characteristic zero, and we get a generalisation of the Jacobson-Morozov theorem: the existence of a pro-reductive envelope $\\Pred(G)$ associated to any affine group scheme $G$ over $K$. Other applications are given in this paper as well as in a forthcoming one on motives.

Dates et versions

hal-00010034 , version 1 (07-10-2005)

Identifiants

Citer

Yves André, Bruno Kahn, Peter O'Sullivan. Nilpotence, radicaux et structures mono\\\"{\\i}dales. Rendiconti del Seminario Matematico della Università di Padova, 2002, 108, pp.107-291. ⟨hal-00010034⟩
83 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More