A structure theory for Jordan H*-pairs
Calderón Martín, A. J. ; González, C. Martín
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 61-77 / Harvested from Biblioteca Digitale Italiana di Matematica
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Jordan H*-pairs appear, in a natural way, in the study of Lie H*-triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie H*-triple systems is reduced to prove the existence of certain L*-algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan H*-pairs to a wide class of Lie H*-triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative H*-pairs, of these pairs. In this paper we give a classification theorem for topologically simple non-quadratic Jordan H*-pairs in terms of associative H*-pairs and certain of their anti-isomorphisms. Some consequences of this classification are also stated.

Il concetto di H*-coppia di Jordan, appare, in modo naturale, nello studio degli H*-sistemi tripli di Lie ([3]). Di fatto, nel [4, Th. 3.1] si prova che il problema della classificazione degli H*-sistemi tripli di Lie si riduce a provare l'esistenza di certi inviluppi di L*-algebre e in [3] si prova anche che è possibile associare H*- coppie topologicamente semplici non quadratiche di Jordan ad un'ampia classe di H*-sistemi tripli di Lie e che poi gli inviluppi precedenti possono essere ottenuti da un'opportuna classificazione, in termini di H*-coppie associative, di queste coppie. In questo lavoro viene dato un teorema di classificazione delle H*-coppie topologicamente semplici non quadratiche di Jordan in termini di H*-coppie associative e di certuni loro anti-isomorfismi. Vengono anche enunciate alcune conseguenze di questa classificazione.

Publié le : 2004-02-01
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Calderón Martín, A. J.; González, C. Martín. A structure theory for Jordan $H^*$-pairs. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 61-77. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_1_61_0/

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