Pseudo-Euclidean Jordan Algebras

REFERENCES

• Aubert , A. ( 1996 ). Structures affines et pseudo-métriques invariantes à gauche sur des groupes de Lie, Thèse, Université Montpellier II .
   Google Scholar
• Bajo , I. , Benayadi , S. , Medina , A. ( 2007 ). Symplectic structures on quadratic Lie algebras . Journal of Algebra 316 ( 1 ): 174 – 188 .
   Web of Science ®Google Scholar
• Bertram , W. ( 2000 ). The Geometry of Jordan and Lie Structures. Lecture Notes in Math. , Vol. 1754 . Berlin : Springer-Verlag .
   Google Scholar
• Bordemann , M. ( 1997 ). Nondegenerate invariant bilinear forms on nonassociative algebras . Acta Math. Univ. Com LXVI (2) pp. 151 – 201 .
   Google Scholar
• Bourbaki , N. ( 1975 ). Groupe et algèbres de Lie. Ch. 7 et 8 , Paris : Hermann .
   Google Scholar
• Diatta , A. , Medina , A. ( 2004 ). Classical Yang-Baxter equation and left invariant affine geometry on Lie groups . Manuscr. Math 114 ( 4 ): 477 – 486 .
   Web of Science ®Google Scholar
• Faraut , J. , Korányi , A. ( 1994 ). Analysis on Symmetric Cones . Oxford : Clarendon Press .
   Google Scholar
• Jacobson , N. , ( 1968 ). Structure and Representations of Jordan Algebras. American Mathematical Society Colloquium Publications , Vol. XXXIX . Providence , R.I. : American Mathematical Society .
   Google Scholar
• Koecher , M. ( 1967 ). Imbedding of Jordan algebras into Lie algebras . I. Amer. J. Math 89 : 787 – 816 .
   Web of Science ®Google Scholar
• Koecher , M. (1968). Imbedding of Jordan algebras into Lie algebras. II. Amer. J. Math 90:476–510.
   Web of Science ®Google Scholar
• McCrimmon , K. ( 2004 ). A Taste of Jordan Algebras. Universitext . New York : Springer-Verlag .
   Google Scholar
• Medina , A. , Revoy , Ph. ( 1985 ). Algèbre de Lie et produit scalaire invariant . Ann. Scient. Ec. Norm. Sup. 4ème série 18 : 553 – 561 .
   Google Scholar
• O'Neill , ( 1983 ). Semi-Riemannian Geometry with Applications to Relativity . New York : Academic Press .
   Google Scholar
• Schafer , R. D. ( 1966 ). An Introduction to Nonassociative Algebras . New York : Academic Press .
   Google Scholar
• Tits , J. ( 1962 ). Une classe d'algèbres de Lie en relation avec les algèbres de Jordan . Nederl. Akad. Wetensch. Proc. Ser. A 65=Indag. Math 24 : 530 – 535 .
   Google Scholar
• Zhelyabin , V. N. ( 2000 ). Jordan D-bialgebras and symplectic forms on Jordan algebras . Siberian Adv. Math 10 ( 2 ): 142 – 150 .
   Google Scholar
• Zhelyabin , V. N. ( 2000/1999 ). On a class of Jordan D-bialgebras . St. Petersbg. Math. J 11 ( 4 ): 589 – 609 ; Translation from Algebra Anal 11 ( 4 ): 64 – 94 .
   Google Scholar
• Communicated by A. Elduque.
   Google Scholar