On constructions of Lie (super) algebras and (, Î)-Freudenthal-Kantor triple systems defined by bilinear forms
(2020) In Journal of Algebra and Its Applications 19(11).- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7f0f8110-cd0f-4d00-afc3-8689c2f6bb25
- author
- Kamiya, Noriaki and Mondoc, Daniel LU
- organization
- publishing date
- 2020-11
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- 3-algebras, complex structure, fundamental identity, Lie (super) algebras, triple systems
- in
- Journal of Algebra and Its Applications
- volume
- 19
- issue
- 11
- article number
- 2050223
- publisher
- World Scientific Publishing
- external identifiers
-
- scopus:85075534438
- ISSN
- 0219-4988
- DOI
- 10.1142/S0219498820502230
- language
- English
- LU publication?
- yes
- id
- 7f0f8110-cd0f-4d00-afc3-8689c2f6bb25
- date added to LUP
- 2019-12-09 10:33:38
- date last changed
- 2022-04-18 19:22:56
@article{7f0f8110-cd0f-4d00-afc3-8689c2f6bb25, abstract = {{<p>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.</p>}}, author = {{Kamiya, Noriaki and Mondoc, Daniel}}, issn = {{0219-4988}}, keywords = {{3-algebras; complex structure; fundamental identity; Lie (super) algebras; triple systems}}, language = {{eng}}, number = {{11}}, publisher = {{World Scientific Publishing}}, series = {{Journal of Algebra and Its Applications}}, title = {{On constructions of Lie (super) algebras and (, Î)-Freudenthal-Kantor triple systems defined by bilinear forms}}, url = {{http://dx.doi.org/10.1142/S0219498820502230}}, doi = {{10.1142/S0219498820502230}}, volume = {{19}}, year = {{2020}}, }