Maximal indexes of Tits algebras
type: Item
instance of: scholarly article
title: Maximal indexes of Tits algebras
zbMATH Open document ID: 0854.20060
published in: Documenta Mathematica
publication date: 1996-09-24T00:00:00Z
full work available at URL: https://eudml.org/doc/225129
full work available at URL: 12.html
review text: Summary: Let \(G\) be a split simply connected semisimple algebraic group over a field \(F\) and let \(C\) be the center of \(G\). It is proved that the maximal index of the Tits algebras of all inner forms of \(G_L\) over all field extensions \(L/F\) corresponding to a given character \(\chi\) of \(C\) equals the greatest common divisor of the dimensions of all representations of \(G\) which are given by the multiplication by \(\chi\) being restricted to \(C\). An application to the discriminant algebra of an algebra with an involution of the second kind is given.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 928983
zbMATH Keywords: split simply connected semisimple algebraic groups
zbMATH Keywords: Tits algebras
zbMATH Keywords: inner forms
zbMATH Keywords: representations
zbMATH Keywords: discriminant algebras
author: Alexander Merkurjev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 928983