On constructions of Lie (super) algebras and (, Î)-Freudenthal-Kantor triple systems defined by bilinear forms

• In this work, we discuss a classification of (,Î)-Freudenthal-Kantor 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 Freudenthal-Kantor triple systems. We also show that we can associate a complex structure into these (,Î)-Freudenthal-Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such (,Î)-Freudenthal-Kantor triple systems and the corresponding Lie (super) algebra construction.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

3-algebras

complex structure

fundamental identity

Lie (super) algebras

triple systems

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art (ämneskategori)

ref (ämneskategori)