Geodesic
A structure theory for Jordan $H^*$-pairs
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 61-77.

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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. 
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Calderón Martín, A. J.; González, C. Martín. A structure theory for Jordan $H^*$-pairs. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 61-77. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a2/

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