Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds

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Abstract

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.

Original languageEnglish
Pages (from-to)563-578
Number of pages16
JournalForum Mathematicum
Volume31
Issue number3
DOIs
Publication statusPublished - 1 May 2019
Externally publishedYes

Keywords

  • Lattice
  • Lie algebras of type I
  • Locally conformal Kähler metric
  • Locally conformal symplectic structure
  • Solvmanifold
  • Vaisman metric

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