论文标题
几乎是阿贝尔谎言组，亚组和商
Almost Abelian Lie groups, subgroups and quotients
论文作者
论文摘要
一个几乎是亚伯式的谎言组是一个非亚伯式的谎言群，具有1 codimension 1 Abelian正常亚组。大多数三维真实的谎言群体几乎都是阿比亚人，它们出现在涉及各向异性媒体的各个地方，宇宙学，晶体学等。在理论物理学和差异几何形状中，几乎是亚洲的谎言群体及其同质空间提供了一些最简单的silvmanifolds，例如当前的semsitrip semsitrip semsitrice exeplice eStiperics kich eysplice eSsiperic of -eastic ersectionk。术语。最近，对几乎Abelian Lie代数进行了分类并进行了详细研究。但是，尚未对几乎阿贝尔谎言群体进行系统的研究，目前的论文专门介绍了对这一广泛而多样化类别的属性的明确描述。 调查的主题是真正几乎是阿贝尔的谎言群体，其谎言群体的理论方面，例如指数图，忠实的矩阵表示，离散和连接的亚组，商和自动形态。重点是对所有技术细节的明确描述。
An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian normal subgroup. The majority of 3-dimensional real Lie groups are almost Abelian, and they appear in all parts of physics that deal with anisotropic media - cosmology, crystallography etc. In theoretical physics and differential geometry, almost Abelian Lie groups and their homogeneous spaces provide some of the simplest solvmanifolds on which a variety of geometric structures such as symplectic, Kähler, spin etc., are currently studied in explicit terms. Recently, almost Abelian Lie algebras were classified and studied in details. However, a systematic investigation of almost Abelian Lie groups has not been carried out yet, and the present paper is devoted to an explicit description of properties of this wide and diverse class of groups. The subject of investigation are real almost Abelian Lie groups with their Lie group theoretical aspects, such as the exponential map, faithful matrix representations, discrete and connected subgroups, quotients and automorphisms. The emphasis is put on explicit description of all technical details.
