Maximal indexes of Tits algebras
Alexander Sergeevich Merkurjev · Documenta Mathematica · 1996
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.