Notes on Chevalley Groups and Root Category I

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.

Publication Details

Journal
ArXiv.org
Published
2025-05-23
Primary Topic
Technology-Enhanced Education Studies
Type
article
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article

Notes on Chevalley Groups and Root Category I

ArXiv.org
Technology-Enhanced Education Studies
article

Notes on Chevalley Groups and Root Category I

article en

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.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 38%
Technology-Enhanced Education Studies
Open Access PDFOpenAlex
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Notes on Chevalley Groups and Root Category I · ArXiv.org (2025) | TGRS Research Map | TGRS