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arXiv · 1012.0402

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

Thomas Bruun Madsen·Andrew Swann
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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.

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Thomas Bruun Madsen, Andrew Swann. 2010-12-02. Homogeneous spaces, multi-moment maps and (2,3)-trivial algebras. https://doi.org/10.1063/1.3599127

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