A new family of homogeneous Einstein manifolds based on symplectic triple systems

TL;DR

This paper introduces a new class of homogeneous Einstein manifolds constructed from simple symplectic triple systems, expanding the understanding of Einstein geometry in semi-Riemannian contexts.

Contribution

It establishes that the standard enveloping Lie algebra and inner derivations of symplectic triple systems form Einstein manifolds, a novel connection in differential geometry.

Findings

Construction of Einstein manifolds from symplectic triple systems

Identification of reductive pairs related to these manifolds

Proof that these manifolds are Einstein

Abstract

For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved that this is an Einstein manifold.