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Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system
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Noriaki Kamiya, Susumu Okubo
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 1 / February 2016

Published online by Cambridge University Press:

13 July 2015, pp. 169-192
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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.

Nondegeneracy for Lie Triple Systems and Kantor Pairs
Esther García, Miguel Gómez Lozano, Erhard Neher
Journal:

Canadian Mathematical Bulletin / Volume 54 / Issue 3 / 01 September 2011

Published online by Cambridge University Press:

20 November 2018, pp. 442-455

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01 September 2011
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We study the transfer of nondegeneracy between Lie triple systems and their standard Lie algebra envelopes as well as between Kantor pairs, their associated Lie triple systems, and their Lie algebra envelopes. We also show that simple Kantor pairs and Lie triple systems in characteristic 0 are nondegenerate.

A CHARACTERIZATION OF (−1, −1)-FREUDENTHAL–KANTOR TRIPLE SYSTEMS
NORIAKI KAMIYA, DANIEL MONDOC, SUSUMU OKUBO
Journal:

Glasgow Mathematical Journal / Volume 53 / Issue 3 / September 2011

Published online by Cambridge University Press:

01 August 2011, pp. 727-738

Print publication:

September 2011
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In this paper, we discuss a connection between (−1, −1)-Freudenthal–Kantor triple systems, anti-structurable algebras, quasi anti-flexible algebras and give examples of such structures. The paper provides the correspondence and characterization of a bilinear product corresponding a triple product.

SIMPLE $(-1,-1)$ BALANCED FREUDENTHAL KANTOR TRIPLE SYSTEMS
ALBERTO ELDUQUE, NORIAKI KAMIYA, SUSUMU OKUBO
Journal:

Glasgow Mathematical Journal / Volume 45 / Issue 2 / May 2003

Published online by Cambridge University Press:

31 July 2003, pp. 353-372

Print publication:

May 2003
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The simple finite dimensional $(-1,-1)$ balanced Freudenthal Kantor triple systems over fields of characteristic zero are classified.

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