Geodesic
Maximal indexes of Tits algebras
Documenta mathematica, Tome 1 (1996), pp. 229-243

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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 GL​ over all field extensions L/F corresponding to a given character χ of C equals the greatest common divisor of the dimensions of all representations of G which are given by the multiplication by χ being restricted to C. An application to the discriminant algebra of an algebra with an involution of the second kind is given.
DOI : 10.4171/dm/12
Classification : 20G15 
A.S. Merkurjev. Maximal indexes of Tits algebras. Documenta mathematica, Tome 1 (1996), pp. 229-243. doi: 10.4171/dm/12
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