Linear Algebraic Groups without the Normalizer Theorem

TL;DR

This paper presents a novel approach to the structure theory of linear algebraic groups that avoids relying on the normalizer theorem, simplifying some foundational aspects.

Contribution

It introduces a method to develop key structural components of linear algebraic groups without using the normalizer theorem, offering a new perspective.

Findings

Structure theory developed without the normalizer theorem

Simplified proofs of root system and Bruhat decomposition

Potential for broader applications in algebraic group theory

Abstract

One can develop the basic structure theory of linear algebraic groups (the root system, Bruhat decomposition, etc.) in a way that bypasses several major steps in the standard development, including the self-normalizing property of Borel subgroups.