Classification of real simple symplectic triple systems

TL;DR

This paper classifies all real simple symplectic triple systems up to isomorphism, providing explicit models and identifying various types including split, unitarian, quaternionic, and exceptional cases.

Contribution

It offers a comprehensive classification and explicit models of all real simple symplectic triple systems, including new non-split types with classical and exceptional enveloping algebras.

Findings

Classification of all real simple symplectic triple systems.

Explicit linear models for each classified system.

Identification of non-split types: unitarian, quaternionic, and exceptional.

Abstract

The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides the split cases, one for each complex simple Lie algebra, there are two kinds of non-split real simple symplectic triple systems with classical enveloping algebra, called unitarian and quaternionic types, and five non-split real simple symplectic triple systems with exceptional enveloping algebra.