On the maximal solvable subgroups of semisimple algebraic groups

TL;DR

This paper classifies all maximal connected solvable subgroups of semisimple algebraic groups over fields of characteristic zero, up to conjugation by rational points, providing a comprehensive understanding of their structure.

Contribution

It offers a complete description of maximal solvable subgroups of semisimple algebraic groups over characteristic zero fields, up to conjugation.

Findings

Classification of all maximal connected solvable subgroups

Description up to conjugation by rational points

Structural insights into semisimple algebraic groups

Abstract

Let $G$ be a semisimple affine algebraic group defined over a field $k$ of characteristic zero. We describe all the maximal connected solvable subgroups of $G$, defined over $k$, up to conjugation by rational points of $G$.