K-Theory for the Leaf Space of Foliations formed by the Generic K-Ornits of some indecomposable $MD_5$-Groups

TL;DR

This paper investigates the K-theory of leaf spaces in certain foliations formed by maximal dimensional K-orbits of specific indecomposable $MD_5$-groups, extending previous topological classifications.

Contribution

It provides an analytical description and characterization of Connes' C*-algebras associated with these foliations using K-functors, advancing the understanding of their K-theoretic properties.

Findings

K-theory applied to leaf spaces of $MD_5$-foliations

Characterization of Connes' C*-algebras for these foliations

Extension of topological classification to K-theoretic analysis

Abstract

The paper is a continuation of the authors' work in which we considered foliations formed by the maximal dimensional K-orbits ($MD_5$-foliations) of connected $MD_5$-groups such that their Lie algebras have 4-dimensional commutative derived ideals and give the topological classification of considered foliations. In this paper, we study K-theory for the leaf space of some from these $MD_5$-foliations and analytically describes and characterized Connes' C*-algebras of considered foliations by the method of K-functors.