论文标题
在五个维度的谎言组上不变的共形杀死yano $ 2 $ forms
Invariant Conformal Killing-Yano $2$-forms on five dimensional Lie Groups
论文作者
论文摘要
我们研究左不变的杀戮Yano（CKY）$ 2 $ - 成形的谎言团体，并具有左不变度度量。我们将所有$ 5 $维度的度量谎言代数分类为带有CKY张量的代数，这些代数被作为4维度量谎言代数的一维中心扩展，并具有可逆的平行偏压对称张量。另一方面，我们还对$ 5 $维度的度量代数进行了分类，其维度的中心大于一个严格的CKY张量。此外，我们确定了这些公制谎言代数的所有可能的CKY张量。特别是，我们展示了CKY $ 2 $ forms的第一个示例，这些示例不承认任何Sasakian结构。
We study left invariant conformal Killing-Yano (CKY) $2$-forms on Lie groups endowed with a left invariant metric. We classify all $5$-dimensional metric Lie algebras carrying CKY tensors that are obtained as a one-dimensional central extension of 4-dimensional metric Lie algebras endowed with a invertible parallel skew-symmetric tensor. On the other hand, we also classify $5$-dimensional metric Lie algebras with center of dimension greater than one admitting strict CKY tensors. In addition, we determine all possible CKY tensors on these metric Lie algebras. In particular, we exhibit the first examples of CKY $2$-forms on metric Lie algebras which do not admit any Sasakian structure.
