Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds
Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds
复制标题
I型李代数及其求解流形上的局部共形辛结构
DOI：
10.1515/forum-2018-0200
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发表时间：
2018
影响因子：
0.8
通讯作者：
M. Origlia
中科院分区：
文献类型：
--
作者：
M. Origlia
We study Lie algebras of type I, that is, a Lie algebra
{\mathfrak{g}}
where all the eigenvalues of the operator
{\operatorname{ad}_{X}}
are imaginary for all
{X\in\mathfrak{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.
