论文标题
在非单明性2步中的磁场上
Magnetic fields on non-singular 2-step nilpotent Lie groups
论文作者
论文摘要
这项工作的目的是研究2步尼尔氏底层的左转磁场。始终保证了中心为非排效机或2形式的内核的封闭2形式的存在，但中心为中心是各向同性的封闭的2形形式的存在是一种特殊情况。这些两种形式称为II型。我们对非单一谎言代数的存在有很大的障碍。此外，我们证明，只有$ h $ type的谎言团体承认II型封闭的2型是真正的，复杂的和Quaternionic Heisenberg Lie lie oftriens lie of 3，六，六和七。我们还证明了在某些假设下均匀的磁场不存在。最后，我们给出了非单明性谎言代数的构造，证明在这些例子的一些家庭中，II型没有封闭的2型。
The aim of this work is the study of left-invariant magnetic fields on 2-step nilpotent Lie groups. While the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is isotropic but not in the kernel of the 2-form, is a special situation. These 2-forms are called of type II. We obtain a strong obstruction for the existence on non-singular Lie algebras. Moreover, we prove that the only $H$-type Lie groups admitting closed 2-forms of type II are the real, complex and quaternionic Heisenberg Lie groups of dimension three, six and seven, respectively. We also prove the non-existence of uniform magnetic fields under certain hypotheses. Finally we give a construction of non-singular Lie algebras, proving that in some families of these examples there are no closed 2-form of type II.
