Abstract
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.
| Original language | English |
|---|---|
| Article number | 2050223 |
| Journal | Journal of Algebra and Its Applications |
| Volume | 19 |
| Issue number | 11 |
| Early online date | 2019 Nov 14 |
| DOIs | |
| Publication status | Published - 2020 Nov |
Subject classification (UKÄ)
- Algebra and Logic
Free keywords
- 3-algebras
- complex structure
- fundamental identity
- Lie (super) algebras
- triple systems