Solvable Lie algebras are not that hypo |
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Authors: | Diego Conti Marisa Fern??ndez Jos?? A Santisteban |
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Institution: | 1. Dipartimento di Matematica e Applicazioni, Universit?? di Milano Bicocca, Via Cozzi 53, 20125, Milano, Italy 2. Facultad de Ciencia y Tecnolog??a, Departamento de Matem??ticas, Universidad del Pa??s Vasco, Apartado 644, 48080, Bilbao, Spain
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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 five-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3).
The choice of a splitting
\mathfrakg* = V1 ?V2 {\mathfrak{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 nonunimodular 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. |
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Keywords: | |
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