Article

Monatshefte für Mathematik

, Volume 86, Issue 2, pp 107-129

Homogeneous algebraic varieties defined by Jordan pairs

  • Ottmar LoosAffiliated withDepartment of Mathematics, University of British Columbia

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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\(\mathfrak{B}\).