$(\epsilon,\delta)$-Freudenthal Kantor triple systems, $\delta$-structurable algebras and Lie superalgebras
(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:
https://lup.lub.lu.se/record/1857155
- author
- Kamiya, Noriaki ; Mondoc, Daniel LU and Okubo, Susumu
- organization
- publishing date
- 2010
- 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
- 2016-04-01 13:22:11
- date last changed
- 2018-11-21 20:15:25
@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}}, keywords = {{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}}, }