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

Noriaki Kamiya, Daniel Mondoc, Susumu Okubo

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)191-206
JournalAlgebras, Groups and Geometries
Volume2
Issue number27
Publication statusPublished - 2010

Subject classification (UKÄ)

  • Mathematical Sciences

Free keywords

  • Lie superalgebras
  • triple systems

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