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$(\epsilon,\delta)$-Freudenthal Kantor triple systems, $\delta$-structurable algebras and Lie superalgebras

Kamiya, Noriaki; Mondoc, Daniel LU and Okubo, Susumu (2010) In Algebras, Groups and Geometries 2(27). p.191-206
Abstract
In this paper we discuss $(\epsilon,\delta)$-Freudenthal Kantor triple systems

with certain structure on the subspace $L_{-2}$ of the corresponding standard

embedding five graded Lie (super)algebra $L(\epsilon,\delta):=L_{-2}\oplus L_{-1}\oplus L_0\oplus L_1\oplus L_2; [L_i,L_j]\subseteq L_{i+j}$. We recall Lie and Jordan structures associated with $(\epsilon,\delta)$-Freudenthal Kantor triple systems (see ref [26],[27]) and we give results for unitary and pseudo-unitary $(\epsilon,\delta)$-Freudenthal Kantor triple systems. Further, we give the notion of $\delta$-structurable algebras and connect them to $(-1,\delta)$-Freudenthal Kantor triple systems and the corresponding Lie (super)

algebra construction.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Lie superalgebras, triple systems
in
Algebras, Groups and Geometries
volume
2
issue
27
pages
191 - 206
publisher
Hadronic Press
ISSN
0741-9937
language
English
LU publication?
yes
id
fb8d3ecb-142e-4783-acce-07d31dc6a43c (old id 1857155)
date added to LUP
2011-05-20 14:11:00
date last changed
2018-05-29 11:44:25
@article{fb8d3ecb-142e-4783-acce-07d31dc6a43c,
  abstract     = {In this paper we discuss $(\epsilon,\delta)$-Freudenthal Kantor triple systems<br/><br>
with certain structure on the subspace $L_{-2}$ of the corresponding standard<br/><br>
embedding five graded Lie (super)algebra $L(\epsilon,\delta):=L_{-2}\oplus L_{-1}\oplus L_0\oplus L_1\oplus L_2; [L_i,L_j]\subseteq L_{i+j}$. We recall Lie and Jordan structures associated with $(\epsilon,\delta)$-Freudenthal Kantor triple systems (see ref [26],[27]) and we give results for unitary and pseudo-unitary $(\epsilon,\delta)$-Freudenthal Kantor triple systems. Further, we give the notion of $\delta$-structurable algebras and connect them to $(-1,\delta)$-Freudenthal Kantor triple systems and the corresponding Lie (super)<br/><br>
algebra construction.},
  author       = {Kamiya, Noriaki and Mondoc, Daniel and Okubo, Susumu},
  issn         = {0741-9937},
  keyword      = {Lie superalgebras,triple systems},
  language     = {eng},
  number       = {27},
  pages        = {191--206},
  publisher    = {Hadronic Press},
  series       = {Algebras, Groups and Geometries},
  title        = {$(\epsilon,\delta)$-Freudenthal Kantor triple systems, $\delta$-structurable algebras and Lie superalgebras},
  volume       = {2},
  year         = {2010},
}