K-theory for the Leaf Space of Foliations Formed by the Generic K-orbits of a class of Solvable Real Lie Groups

TL;DR

This paper investigates the K-theory of leaf spaces in MD5-foliations of certain solvable Lie groups, extending previous classifications and characterizations of their associated C*-algebras using K-functors.

Contribution

It provides a comprehensive K-theoretic analysis of all MD5-foliations classified in prior work, and characterizes their Connes' C*-algebras via K-functors.

Findings

K-theory computed for leaf spaces of MD5-foliations

Connes' C*-algebras characterized using K-functors

Extension of previous classification results

Abstract

The paper is a continuation of the works [17] of Vu and Shum, [18] and [19] of Vu and Hoa. In [17], Vu and Shum classified all the MD5-algebras having commutative derived ideals. In [18], Vu and Hoa considered foliations formed by the maximal dimensional K-orbits (for short, MD5-foliations) of connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideals and gave a topological classification of the considered foliations. In [19], Vu and Hoa characterized the Connes' C*-algebras of some MD5-foliations considered in \cite{VU-HO09} by the method of K-functors. In this paper, we study K-theory for the leaf space of all MD5-foliations which are classified in [18] and characterize the Connes' C*-algebras of them by the method of K-functors.