Maximal indexes of Tits algebras

  • A.S. Merkurjev

    00131 D 33501 Bielefeld Germany
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Abstract

Let be a split simply connected semisimple algebraic group over a field and let be the center of . It is proved that the maximal index of the Tits algebras of all inner forms of over all field extensions corresponding to a given character of equals the greatest common divisor of the dimensions of all representations of which are given by the multiplication by being restricted to . An application to the discriminant algebra of an algebra with an involution of the second kind is given.

Cite this article

A.S. Merkurjev, Maximal indexes of Tits algebras. Doc. Math. 1 (1996), pp. 229–243

DOI 10.4171/DM/12