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  • Tits‘ Constructions of Jordan Algebras and F4 Bundles on the Plane

  • R. PARIMALA, R. SRIDHARAN, MANEESH L. THAKUR
  • Journal:
    Compositio Mathematica / Volume 119 / Issue 1 / October 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 13-40
    Print publication:
    October 1999
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  • In this paper, constructions of Jordan algebras over commutative rings are given which place, within a general set-up, the classical Tits constructions of exceptional central simple Jordan algebras over fields. These are used to exhibit nontrivial Jordan algebra bundles over the affine plane with a given exceptional Jordan division algebra over k as the fibre. The associated principal F$_4$ bundles are shown to admit no reduction of the structure group to any proper connected reductive subgroup.