On conjugacy classes of maximal tori in classical groups
type: Item
instance of: scholarly article
title: On conjugacy classes of maximal tori in classical groups
zbMATH Open document ID: 0682.20031
DOI: 10.1016/0021-8693(89)90297-4
author: Kazutoshi Kariyama
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let K be an infinite field and SL, Sp, SO are classical algebraic groups defined over K. In the paper a complete classification of the K-conjugacy classes of maximal K-tori in these groups is given. Let G be such a classical group, for each K-conjugacy class of maximal K-tori of G, a K- isomorphism class of commutative semi-simple K-algebras with involutions is naturally obtained and the image of this correspondence is determined. Furthermore for each K-isomorphism class of such K-algebras in its image, the cardinality of all conjugacy classes of maximal K-tori of G corresponding to it is calculated.
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 4116811
zbMATH Keywords: algebraic groups
zbMATH Keywords: conjugacy classes of maximal K-tori
zbMATH Keywords: semi-simple K- algebras with involutions
reviewed by: V. I. Yanchevskiĭ
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90297-4
OpenAlex ID: W2080475110
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description: scientific article; zbMATH DE number 4116811