Homogeneous spaces, multi-moment maps and (2,3)-trivial algebras

Abstract

For geometries with a closed three-form we briefly overview the notion of multi-moment maps. We then give concrete examples of multi-moment maps for homogeneous hypercomplex and nearly Kaehler manifolds. A special role in the theory is played by Lie algebras with second and third Betti numbers equal to zero. These we call (2,3)-trivial. We provide a number of examples of such algebras including a complete list in dimensions up to and including five.

Cited by in corpus (2)

• Closed forms and multi-moment maps
• Remarks on Hamiltonian Structures in G_2-Geometry