We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1\oplus V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.

Conti, D., Fernàndez, M., Santisteban, J. (2011). Solvable Lie algebras are not that hypo. TRANSFORMATION GROUPS, 16(1), 51-69 [10.1007/s00031-011-9127-8].

Solvable Lie algebras are not that hypo

CONTI, DIEGO;
2011

Abstract

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1\oplus V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.
Articolo in rivista - Articolo scientifico
Solvable Lie algebras, hypo structures
English
2011
16
1
51
69
open
Conti, D., Fernàndez, M., Santisteban, J. (2011). Solvable Lie algebras are not that hypo. TRANSFORMATION GROUPS, 16(1), 51-69 [10.1007/s00031-011-9127-8].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/20711
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