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Tits‘ Constructions of Jordan Algebras and F4 Bundles on the Plane
Published online by Cambridge University Press: 04 December 2007
Abstract
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.
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- © 1999 Kluwer Academic Publishers
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