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Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system

Part of: Jordan algebras General nonassociative rings Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  13 July 2015

Noriaki Kamiya  and
Susumu Okubo
Noriaki Kamiya
Affiliation:
Department of Mathematics, University of Aizu, Aizuwakamatsu, Japan (kamiya@u-aizu.ac.jp)
Susumu Okubo
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA (okubo@pas.rochester.edu)
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Abstract

Symmetry groups of Lie algebras and superalgebras constructed from (∈, δ)-Freudenthal-Kantor triple systems have been studied. In particular, for a special (ε, ε)-Freudenthal–Kantor triple, it is the SL(2) group. Also, the relationship between two constructions of Lie algebras from structurable algebras has been investigated.

Keywords

triple systemsLie algebrassymmetry group

MSC classification

Secondary: 17C50: Jordan structures associated with other structures 17A40: Ternary compositions 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 169 - 192
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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