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On constructions of Lie (super) algebras and $(𝜀, δ)$ $(𝜀, δ)$ -Freudenthal–Kantor triple systems defined by bilinear forms

Noriaki Kamiya

http://orcid.org/0000-0002-4788-163X

Center for Mathematical Sciences, University of Aizu, 965-8580 Japan

E-mail Address: shigekamiya@outlook.jp

Corresponding author.

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and

Daniel Mondoc

Centre for Mathematical Sciences, Lund University, 22 100 Lund, Sweden

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https://doi.org/10.1142/S0219498820502230Cited by:2 (Source: Crossref)

Abstract

In this work, we discuss a classification of $(𝜖, δ)$ $(𝜖, δ)$ -Freudenthal–Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal–Kantor triple systems. We also show that we can associate a complex structure into these ( $𝜀, δ)$ $𝜀, δ)$ -Freudenthal–Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such $(𝜀, δ)$ $(𝜀, δ)$ -Freudenthal–Kantor triple systems and the corresponding Lie (super) algebra construction.

Communicated by L. A. Bokut

Keywords:

AMSC: 17A40, 17B60, 17C05

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