Abstract

In this paper, we study a Peirce decomposition for (-1,-1)-Freudenthal-Kantor triple sys- tems and give several examples.

Highlights

  • Our aim is to give a characterization of many mathematical and physical fields by means of concept of triple systems

  • In this paper, we study a Peirce decomposition for (-1,1)-Freudenthal-Kantor triple systems and give several examples. 2000 MSC: 17A40

  • It seems that such concept is useful to an application of nonassociative algebras as well as the characterization of Yang-Baxter equations, and the construction of Liealgebras and Jordanalgebras ([3]-[10], [12], [13], [15])

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Summary

Introduction

Our aim is to give a characterization of many mathematical and physical fields by means of concept of triple systems (here, triple systems mean a vector space equipped with a triple product < xyz >). It seems that such concept is useful to an application of nonassociative algebras as well as the characterization of Yang-Baxter equations, and the construction of Lie (super)algebras and Jordan (super)algebras ([3]-[10], [12], [13], [15]).

The triple products are generally denoted by
Thus it follows that
Thus we get
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