Maximal indexes of Tits algebras
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.
split simply connected semisimple algebraic groups
scientific article; zbMATH DE number 928983
scientific article