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

Kamiya, Noriaki and Mondoc, Daniel LU (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.

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author
and
organization
publishing date
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}},
}