Geodesic
Conjugacy Classes of n-Tuples in Semi-Simple Jordan Algebras
Journal of Lie theory, Tome 25 (2015) no. 2, pp. 443-458
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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.
Classification : 17C20, 17C30
Mots-clés : Semi-simple Jordan algebra, automorphism group, closed orbit 
@article{JLT_2015_25_2_JLT_2015_25_2_a6,
     author = {H. Bergner},
     title = {Conjugacy {Classes} of {n-Tuples} in {Semi-Simple} {Jordan} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {443--458},
     year = {2015},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a6/}
}
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H. Bergner. Conjugacy Classes of n-Tuples in Semi-Simple Jordan Algebras. Journal of Lie theory, Tome 25 (2015) no. 2, pp. 443-458. http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a6/