Measurable Foliations Associated to the Coadjoint Representation of a Class of Seven-Dimensional Solvable Lie Groups

IF 0.5 Q4 PHYSICS, MATHEMATICAL
V. Le, Tu T. C. Nguyen, T. Nguyen
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引用次数: 0

Abstract

We consider connected and simply connected seven-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2}$ of Dixmier. First, we give geometric descriptions of the maximal-dimensional orbits in the coadjoint representation of all considered Lie groups. Next, we prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. Finally, the topological classification of all these foliations is also provided.
一类七维可解李群的伴表示的可测叶
我们考虑李代数具有Dixmier的幂零根$\g_{5,2}$的连通和单连通七维李群。首先,我们给出了所有考虑的李群的共点表示中的最大维轨道的几何描述。接下来,我们证明,对于每一个考虑的群,一般共点轨道族在Connes意义上形成了一个可测量的叶理。最后,给出了所有这些叶理的拓扑分类。
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来源期刊
CiteScore
1.50
自引率
25.00%
发文量
3
期刊介绍: The Journal of Geometry and Symmetry in Physics is a fully-refereed, independent international journal. It aims to facilitate the rapid dissemination, at low cost, of original research articles reporting interesting and potentially important ideas, and invited review articles providing background, perspectives, and useful sources of reference material. In addition to such contributions, the journal welcomes extended versions of talks in the area of geometry of classical and quantum systems delivered at the annual conferences on Geometry, Integrability and Quantization in Bulgaria. An overall idea is to provide a forum for an exchange of information, ideas and inspiration and further development of the international collaboration. The potential authors are kindly invited to submit their papers for consideraion in this Journal either to one of the Associate Editors listed below or to someone of the Editors of the Proceedings series whose expertise covers the research topic, and with whom the author can communicate effectively, or directly to the JGSP Editorial Office at the address given below. More details regarding submission of papers can be found by clicking on "Notes for Authors" button above. The publication program foresees four quarterly issues per year of approximately 128 pages each.
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