Maximal indexes of Tits algebras

  • A.S. Merkurjev

    00131 D 33501 Bielefeld Germany
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Let GG be a split simply connected semisimple algebraic group over a field FF and let CC be the center of GG. It is proved that the maximal index of the Tits algebras of all inner forms of GLG_L over all field extensions L/FL/F corresponding to a given character χ\chi of CC equals the greatest common divisor of the dimensions of all representations of GG which are given by the multiplication by χ\chi being restricted to CC. An application to the discriminant algebra of an algebra with an involution of the second kind is given.

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

DOI 10.4171/DM/12