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Homogeneous algebraic varieties defined by Jordan pairs
Authors:Prof. Ottmar Loos
Affiliation:(1) Department of Mathematics, University of British Columbia, V6T 1W5 Vancouver, B. C., Canada;(2) Present address: Institut für Mathematik, Universität Innsbruck, Innrain 52, A-6020 Innsbruck, Austria
Abstract:
Every Jordan pair
$$mathfrak{B} = (mathfrak{B}^ +  ,mathfrak{B}^ -  )$$
defines an algebraic varietyX containing
$$mathfrak{B}^ +$$
as a dense open subset.X is projective (affine) if and only if
$$mathfrak{B}$$
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
$$mathfrak{B}$$
. If
$$mathfrak{B}$$
is separable then the automorphism group ofX is the projective group of
$$mathfrak{B}$$
.
Keywords:
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