On compact realifications of exceptional simple Kantor triple systems
(2007) In Journal of Generalized Lie Theory and Applications 1(1). p.29-40- Abstract
- Let A be the realification of the matrix algebra determined by Jordan algebra of hermitian
matrices of order three over a complex composition algebra. We define an involutive
automorphism on A with a certain action on the triple system obtained from A which give
models of simple compact Kantor triple systems. In addition, we give an explicit formula
for the canonical trace form and the classification for these triples and their corresponding
exceptional real simple Lie algebras. Moreover, we present all realifications of complex exceptional
simple Lie algebras as Kantor algebras for a compact simple Kantor triple system
defined on a structurable algebra of skew-dimension one.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1670167
- author
- Mondoc, Daniel LU
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- graded Lie algebras, structurable algebras, triple systems
- in
- Journal of Generalized Lie Theory and Applications
- volume
- 1
- issue
- 1
- pages
- 29 - 40
- publisher
- Ashdin Publishing
- ISSN
- 1736-5279
- language
- English
- LU publication?
- no
- id
- f414feb2-d2ff-42c3-9fa7-e1d21caf0c3a (old id 1670167)
- alternative location
- http://www.ashdin.com/journals/jglta/2007/1/issue1.aspx
- date added to LUP
- 2016-04-01 12:23:12
- date last changed
- 2022-01-27 02:59:53
@article{f414feb2-d2ff-42c3-9fa7-e1d21caf0c3a, abstract = {{Let A be the realification of the matrix algebra determined by Jordan algebra of hermitian<br/><br> matrices of order three over a complex composition algebra. We define an involutive<br/><br> automorphism on A with a certain action on the triple system obtained from A which give<br/><br> models of simple compact Kantor triple systems. In addition, we give an explicit formula<br/><br> for the canonical trace form and the classification for these triples and their corresponding<br/><br> exceptional real simple Lie algebras. Moreover, we present all realifications of complex exceptional<br/><br> simple Lie algebras as Kantor algebras for a compact simple Kantor triple system<br/><br> defined on a structurable algebra of skew-dimension one.}}, author = {{Mondoc, Daniel}}, issn = {{1736-5279}}, keywords = {{graded Lie algebras; structurable algebras; triple systems}}, language = {{eng}}, number = {{1}}, pages = {{29--40}}, publisher = {{Ashdin Publishing}}, series = {{Journal of Generalized Lie Theory and Applications}}, title = {{On compact realifications of exceptional simple Kantor triple systems}}, url = {{http://www.ashdin.com/journals/jglta/2007/1/issue1.aspx}}, volume = {{1}}, year = {{2007}}, }