On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms
| Autor: | Daniel Mondoc, Noriaki Kamiya |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Applied Mathematics Mathematics::Rings and Algebras 010102 general mathematics Structure (category theory) 0102 computer and information sciences Bilinear form 01 natural sciences 010201 computation theory & mathematics Simple (abstract algebra) Lie algebra 0101 mathematics Algebra over a field Mathematics::Representation Theory Mathematics |
| Zdroj: | Journal of Algebra and Its Applications. 19:2050223 |
| ISSN: | 1793-6829 0219-4988 |
| DOI: | 10.1142/s0219498820502230 |
| Popis: | In this work, we discuss a classification of [Formula: see text]-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 ([Formula: see text]-Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such [Formula: see text]-Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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