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A STRUCTURE THEORY OF (−1,−1)-FREUDENTHAL KANTOR TRIPLE SYSTEMS

Part of: General nonassociative rings Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  02 October 2009

NORIAKI KAMIYA ,
DANIEL MONDOC  and
SUSUMU OKUBO
NORIAKI KAMIYA
Affiliation:
Center for Mathematical Sciences, University of Aizu, 965-8580 Aizuwakamatsu, Japan (email: [email protected])
DANIEL MONDOC*
Affiliation:
Centre for Mathematical Sciences, Lund University, 22 100 Lund, Sweden (email: [email protected])
SUSUMU OKUBO
Affiliation:
Department of Physics, University of Rochester, Rochester, NY 14627, USA (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper we discuss the simplicity criteria of (−1,−1)-Freudenthal Kantor triple systems and give examples of such triple systems, from which we can construct some Lie superalgebras. We also show that we can associate a Jordan triple system to any (ε,δ)-Freudenthal Kantor triple system. Further, we introduce the notion of δ-structurable algebras and connect them to (−1,δ)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction.

Keywords

Lie superalgebrastriple systems

MSC classification

Secondary: 17A40: Ternary compositions 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 132 - 155
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The first author’s research was partially supported by Grant-in-Aid for Scientific Research (No. 19540042 (C),(2)), Japan Society for the Promotion of Science. The second author’s research was partially supported by Japan Society for the Promotion of Science (No. PE 07601). The third author’s research was supported by U.S. Department of Energy Grant No. DE-FG02-91ER40685.

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