Algorithm for Lang's Theorem

2005/06/03 by Arjeh M. Cohen, Cohen, Arjeh M., Scott H. Murray +1
Computer Science · Mathematics · #20-04 #20G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.AG #math.GR #msc:20-04 #msc:20G40

paper · pdf · doi:10.48550/arxiv.math/0506068

arxiv created 2005/06/03 · openalex publication_date 2005/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie type. We use an algorithm for computing a Chevalley basis for a split reductive Lie algebra, which is of independent interest.

Related

• Langlands parameters for reductive groups over finite fields
• An LLL algorithm with symmetries
• Reductive groups and Steinberg maps
• Finite Langlands correspondence
• A comparison of L-groups for covers of split reductive groups