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

Published online by Cambridge University Press:  04 December 2007

R. PARIMALA ,
R. SRIDHARAN  and
MANEESH L. THAKUR
R. PARIMALA
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India. e-mail: parimala@tifrvax.tifr.res.in/sridhar@tifrvax.tifr.res.in/maneesh@tifrvax.tifr.res.in
R. SRIDHARAN
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India. e-mail: parimala@tifrvax.tifr.res.in/sridhar@tifrvax.tifr.res.in/maneesh@tifrvax.tifr.res.in
MANEESH L. THAKUR
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India. e-mail: parimala@tifrvax.tifr.res.in/sridhar@tifrvax.tifr.res.in/maneesh@tifrvax.tifr.res.in
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Abstract

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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.

Keywords

exceptional Jodan algebrasF$_4$ bundles.
Type
Research Article
Information
Compositio Mathematica , Volume 119 , Issue 1 , October 1999 , pp. 13 - 40
Copyright
© 1999 Kluwer Academic Publishers