Prolongations of Lie algebras and applications

By P. Nagy. 2007

60 citations recorded by the source corpus.

We study the skew-symmetric prolongation of a Lie subalgebra $\g \subseteq \mathfrak{so}(n)$, in other words the intersection $\Lambda^3 \cap (\Lambda^1 \otimes \g)$.We compute this space in full generality. Applications include uniqueness results for connections with skew-symmetric torsion and also the proof of the Euclidean version of a conjecture posed in \cite{ofarill} concerning a class of Pl\"ucker-type embeddings. We also derive a classification of the metric k-Lie algebras (or Filipov algebras), in positive signature and finite dimension. Prolongations of Lie algebras can also be used to finish the classification, started in \cite{datri}, of manifolds admitting Killing frames, or equivalently flat connections with 3-form torsion. Next we study specific properties of invariant 4-forms of a given metric representation and apply these considerations to classify the holonomy representation of metric connections with vectorial torsion, that is with torsion contained in $\Lambda^1 \subseteq \Lambda^1 \otimes \Lambda^2$.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d930048bf70f67225bc8a691c87bdf7a78fe867

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In Applied Mathematics

1. J. Gutowski
2. J. Gauntlett
3. J. Sparks
4. D. Martelli

In Geometry and Topology

1. J. Gutowski
2. J. Gauntlett
3. J. Sparks
4. D. Martelli

In Mathematical Physics

1. J. Gutowski
2. J. Gauntlett

Citations in the corpus

• Constraining Maximally Supersymmetric Membrane Actions (2008, result): “After this paper was submitted for publication, we became aware of [22], which claims the same result using a different approach.”