Merkurjev, A. S. Maximal indexes of Tits algebras. (English) Zbl 0854.20060 Doc. Math. 1, 229-243 (1996). 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. Cited in 1 ReviewCited in 8 Documents MSC: 20G15 Linear algebraic groups over arbitrary fields 14F22 Brauer groups of schemes 20G05 Representation theory for linear algebraic groups 16W10 Rings with involution; Lie, Jordan and other nonassociative structures Keywords:split simply connected semisimple algebraic groups; Tits algebras; inner forms; representations; discriminant algebras PDFBibTeX XMLCite \textit{A. S. Merkurjev}, Doc. Math. 1, 229--243 (1996; Zbl 0854.20060) Full Text: EuDML EMIS