Abstract
In this work, we discuss a classification of [Formula: see text]-FreudenthalâKantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their FreudenthalâKantor triple systems. We also show that we can associate a complex structure into these ([Formula: see text]-FreudenthalâKantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-FreudenthalâKantor triple systems and the corresponding Lie (super) algebra construction.
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