On the computation of conjugacy classes of Chevalley groups
type: Item
instance of: scholarly article
title: On the computation of conjugacy classes of Chevalley groups
zbMATH Open document ID: 0882.20031
DOI: 10.1007/BF01190331
author: Peter Fleischmann
author: Ingo Janiszczak
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1998-03-10T00:00:00Z
review text: Let \(G\) be a connected reductive algebraic group defined over a Galois field \(F_q\) with corresponding Frobenius endomorphism \(F\) and a finite group \(G^F\) of \(F\)-fixed points. Two semisimple conjugacy classes \([s_1]\) and \([s_2]\) of \(G^F\) are called of the same genus if the centralizers \(C_G(s_1)\) and \(C_G(s_2)\) are conjugate under \(G^F\). An equivalence class is called a genus number. In this paper an algorithm is given to determine the number of semisimple conjugacy classes for a given centralizer type for the Chevalley groups \(\text{SL}_n(q)\) and \(\text{SU}_n(q)\). The authors determine the exact number of regular semisimple classes of these groups. They use Jordan decomposition to summarize results pertaining to the generic class number of exceptional Chevalley groups of adjoint type.
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20C40
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 878205
zbMATH Keywords: connected reductive algebraic groups
zbMATH Keywords: Frobenius endomorphisms
zbMATH Keywords: semisimple conjugacy classes
zbMATH Keywords: centralizers
zbMATH Keywords: genus numbers
zbMATH Keywords: algorithms
zbMATH Keywords: Chevalley groups
zbMATH Keywords: numbers of regular semisimple classes
zbMATH Keywords: generic class numbers
zbMATH Keywords: exceptional Chevalley groups
reviewed by: Qaiser Mushtaq
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01190331
OpenAlex ID: W2024669488
description: scientific article; zbMATH DE number 878205