Un scindage du morphisme de Frobenius sur l'alg\`ebre des distributions d'un groupe r\'eductif

TL;DR

This paper extends the construction of a Frobenius splitting from simply connected semisimple algebraic groups to all reductive groups over algebraically closed fields of positive characteristic, with implications for their distribution algebras.

Contribution

It generalizes the Frobenius splitting construction from simply connected semisimple groups to all reductive groups, broadening its applicability.

Findings

Constructed a Frobenius splitting for the algebra of distributions of reductive groups.

Derived corollaries related to the structure and properties of these groups.

Extended previous results to a more general class of algebraic groups.

Abstract

For a simply connected semisimple algebraic group over an algebraically closed field of positive characteristic we have already constructed a splitting of the Frobenius endomorphism on its algebra of distributions. We generalize the construction to the case of general reductive groups and derive the corresponding corollaries.