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Examples of Peirce's decomposition associated with simple generalized Jordan triple systems of the second order

Kamiya N.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 2

159-175

The aim of this article is to provide examples of Peirce's decomposition associated with simple generalized Jordan triple systems of the second order. The concept of triple systems has been derived from a construction of simple Lie algebras. Our investigation seeks to characterize the internal structure of triple systems. In particular, we shall study the tripotent elements in the Jordan triple systems associated with generalized Jordan triple systems of the second order.

On a realization of the exceptional simple graded Lie algebras of the second kind and Freudenthal-Kantor systems

Kamiya N.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

55-65

In this paper, from a construction of the standard embedding Lie algebras associated with triple systems, we derive the connection of our earlier work with the study of exceptional real simple Lie algebras of the second kind.