caa a22 4500 445862203 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00031-011-9127-8 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9127-8 Solvable Lie algebras are not that hypo [Elektronische Daten] [Diego Conti, Marisa Fernández, José Santisteban] 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 $ {\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. Springer Science+Business Media, LLC, 2011 53C25 (primary) nationallicence 53C15, 17B30, 53D15 (secondary) nationallicence Conti Diego Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 53, 20125, Milano, Italy aut Fernández Marisa Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain aut Santisteban José Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain aut Transformation Groups SP Birkhäuser Verlag Boston 16/1(2011-03-01), 51-69 1083-4362 16:1<51 2011 16 31 https://doi.org/10.1007/s00031-011-9127-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9127-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Conti Diego Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 53, 20125, Milano, Italy aut NATIONALLICENCE 700 1- Fernández Marisa Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain aut NATIONALLICENCE 700 1- Santisteban José Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/1(2011-03-01), 51-69 1083-4362 16:1<51 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer