Orbit Decomposition of Jordan Matrix Algebras of Order Three under the Automorphism Groups

J. Math. Sci. Univ. Tokyo
Vol. 17 (2010), No. 4, Page 387--417.

Nishio, Akihiro; Yasukur, Osami
Orbit Decomposition of Jordan Matrix Algebras of Order Three under the Automorphism Groups
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Abstract:
The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification, explicitly, in terms of the cross product of H.~Freudenthal and the characteristic polynomial.

Mathematics Subject Classification (2010): Primary 17C30, Secondary 20G41, 57S20.
Received: 2010-07-21