Notes on Chevalley Groups and Root Category I
Buyan Li, Jie Xiao

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.
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