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Journal of Lie Theory 25 (2015), No. 2, 443--458
Copyright Heldermann Verlag 2015

Conjugacy Classes of n-Tuples in Semi-Simple Jordan Algebras

Hannah Bergner
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany

Let J be a finite-dimensional semi-simple Jordan algebra over an algebraically closed field of characteristic 0. In this article, the diagonal action of the automorphism group of J on the n-fold product J × ... × J is studied. In particular, it is shown that the orbit through an n-tuple x = (x1, ..., xn) is closed if and only if the Jordan subalgebra generated by the elements x1, ..., xn is semi-simple.

Keywords: Semi-simple Jordan algebra, automorphism group, closed orbit.

MSC: 17C20, 17C30

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