Lie–Yamaguti algebras related to image

Lie–Yamaguti algebras (or generalized Lie triple systems) are intimately related to reductive homogeneous spaces. Simple Lie–Yamaguti algebras whose standard enveloping Lie algebra is the simple Lie algebra of type G2 are described, making use of the octonions. These examples reveal the much greater complexity of these systems, compared to Lie triple systems.