Abstract
This work, jointly with [7], gives a complete classification of Jordan H*-triple systems. There, the infinite—dimensional topologically simple special nonquadratic Jordan H*-triple systems are fully described in terms of the odd part of a ℤ2—graded H*—algebra. Here we complete the structure theory endowing to any simple finite—dimensional real Jordan triple system, of an H*—structure, essentialy unique, and determining the ones of quadratic type.
This work has been partially supported by the “Plan Andaluz de Investigación y Desarrollo Tecnológico” and the DGICYT with project no. PS89-0119.
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References
Bouhya K. and Fernández, A.:, ‘Jordan-*-triples with minimal inner ideals and compact JB*-triples’, to appear in Proc. London Math. Soc.
Castellón A. and Cuenca J.A.: 1992, ’Alternative H*-triple systems’, Comm. in Algebra 20 (11), 3191–3260.
Castellón A. and Cuenca J.A.: 1992, ’Associative H*-triple systems’, Workshop on Nonassociative Algebraic Models (eds. Gonzalez S. and Myung H.C.), New York.
Castellón A. and Cuenca J.A.: 1993, ’Centroid and metacentroid of an H*-triple system’, Bulletin de la Societé Mathematique de Belgique vol. 45 fascicules 1–2 seria A, 85–91.
Castellón A. and Cuenca J.A.: 1990, ’Compatibility in Jordan H*-triple systems’, Boll. UMI 7(4-B), 433, 477.
Castellón A. and Cuenca J.A.: 1992, ’Isomorphisms of H*-triple systems’, Analli della Scuola Normale Superiore di Pisa, 507–514.
Castellón A., Cuenca J.A. and Martin C.:, ’Special Jordan H*-triple systems’, III International Conference on Nonassociative Algebras and its Applications, Oviedo, 1993, preprint.
Castellón A., Cuenca J.A. and Martin C.: 1992, ’Ternary H*-algebras’, Boll UMI 7 (6-B), 217–228.
Cuenca J.A. and Martin C.: 1992, ’Jordan two-graded H*-algebras’, Workshop on Nonassociative Algebraic Models (eds. Gonzalez S. and Myung H.C.), Nova Science Publishers, New York.
Cuenca J.A. and Sanchez A.:, ’Structure theory for real noncommutative Jordan H*- algebras’, to appear in Journal of Algebra.
Loos O.: 1972, ’Alternative tripelsysteme’, Math. Ann. 198, 205–238.
Loos O.:1971, ‘Lectures on Jordan triples’, Lecture Notes, University of British Columbia, Vancouver.
Neher E.: 1981, ’Klassifikation der einfachen Ausnahme Jordan-Tripelsysteme’, J. Reine Angew. Math. 322.
Rodriguez A.:, ’Jordan Structures in Analysis’, In Proceedings of the 1992 Oberwolfach Conference on Jordan Algebras (to appear).
Zel’manov E.I.: 1983, ’Primary Jordan triple systems I’, Sib. Math. Zh. 24 No. 4, 23–27.
Zel’manov E.I.: 1984, ’Primary Jordan triple systems II’, Sib. Math. Zh. 25 No. 5, 60–51.
Zel’manov E.I.: 1985, ’Primary Jordan triple systems III’, Sib. Math. Zh. 26 No. 1, 71–82.
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© 1994 Springer Science+Business Media Dordrecht
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Serrano, A.C., Mira, J.A.C., González, C.M. (1994). Jordan H*-Triple Systems. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_11
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DOI: https://doi.org/10.1007/978-94-011-0990-1_11
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