Notes on Chevalley Groups and Root Category I

TL;DR

This paper constructs Chevalley groups from root categories, proves their Bruhat decomposition and simplicity, and calculates the orders of finite Chevalley groups, advancing the understanding of their algebraic structure.

Contribution

It introduces a new construction of Chevalley groups using root categories and establishes key properties like Bruhat decomposition and simplicity.

Findings

Proved Bruhat decomposition for Chevalley groups

Established the simplicity of Chevalley groups

Calculated orders of finite Chevalley groups

Abstract

Based on the construction of simple Lie algebras via root category and following Chevalley's results, we construct Chevalley groups from the root category. Then we prove the Bruhat decomposition and the simplicity of the Chevalley groups, and calculate the orders of finite Chevalley groups.