Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
We study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/125022 |
| Acceso en línea: | http://hdl.handle.net/11336/125022 |
| Access Level: | acceso abierto |
| Palabra clave: | LATTICE LIE ALGEBRAS OF TYPE I LOCALLY CONFORMAL KÄHLER METRIC LOCALLY CONFORMAL SYMPLECTIC STRUCTURE SOLVMANIFOLD VAISMAN METRIC https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure. |
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