Foliations formed by generic coadjoint orbits of a class of 7-dimensional real solvable Lie groups

Abstract

In this paper, we consider exponential, connected and simply connected Lie groups which are corresponding to Lie algebras of dimension 7 such that the nilradical of them is 5-dimensional nilpotent Lie algebra ${\mathfrak{g}}_{5,2}$ in Table 1. In particular, we give a description of the geometry of the generic orbits in the coadjoint representation of some considered Lie groups. We prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. The topological classification of these foliations is also provided.

47 pages, 1 figure, 5 tables. arXiv admin note: text overlap with arXiv:2105.00536

References in corpus (3)

• All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
• The Geometry of K-Orbits of a Subclass of MD5-Groups and Foliations Formed by their Generic K-Orbits
• K-theory for the Leaf Space of Foliations Formed by the Generic K-orbits of a class of Solvable Real Lie Groups