Some structure theory for a class of triple systems
Nora C. Hopkins
Trans. Amer. Math. Soc. 289 (1985), 203-212
Primary 17A40; Secondary 17A60
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Abstract: This paper deals with a class of triple systems satisfying two generalized five linear identities and having nondegenerate bilinear forms with certain properties. If is such a triple system with bilinear form , it is shown that if is semisimple, then is the direct sum of simple ideals if is symmetric or symplectic or if is completely reducible as a module for its right multiplication algebra . It is also shown that if is a completely reducible -module, is the direct sum of a semisimple ideal and the center of .
Such triple systems can be embedded into certain nonassociative algebras and the results on the triple systems are extended to these algebras.
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