Abstract
In [8] Loos obtains a structure theorem for finite dimensional simple alternative triple systems over an algebraically closed field of characteristic ≠ 2. This theorem has been generalized in [10] (resp. [9]) for simple alternative triple systems (resp. alternative pairs) containing a maximal tripotent (resp. a maximal idempotent). Other classes of alternative triple systems without maximal tripotent over a Hilbert space (real or complex) have been characterized in [2] and [3] where the simplicity is replaced by the topological simplicity and other hypothesis involving an involution and the inner product. In this paper, we obtain a description of nondegenerate prime alternative triple systems containing a maximal tripotent in terms of its central closure. A socle theory for prime nondegenerate alternative triple systems with maximal tripotent is established in a forthcoming paper [4].
This work has been partially supported by the ”Plan Andaluz de Investigación y desarrollo tecnoldgico” and the DGICYT with project no. PS89-0119
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© 1994 Springer Science+Business Media Dordrecht
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Serrano, A.C., González, C.M. (1994). Prime Alternative 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_12
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DOI: https://doi.org/10.1007/978-94-011-0990-1_12
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