A structure theory for Jordan $H^*$-pairs

Calderón Martín, A. J. ; González, C. Martín

Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 61-77

Résumé

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.