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Vietnam
Journal of Mathematics 38:2 (2010) 249-259
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K-Theory
of the Leaf Space of Foliations Formed by the Generic K-Orbits of
Some Indecomposable MD5-Group
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Le Anh Vu and Duong
Quang Hoa
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Abstract. The paper is a continuation of the
authors' work [18]. In [18], we consider foliations formed by the maximal
dimensional K-orbits (MD5-foliations) of
connected MD5-groups
such that their Lie algebras have 4-dimensional commutative derived ideals
and give a topological classification of the considered foliations. In this
paper, we study K-theory of the
leaf space of some of these MD5-foliations
and analytically describe and characterize the Connes' C*-algebras of the considered foliations by the method of K-functors.
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2000 Mathematics Subject Classification: Primary 22E45;
Secondary 46E25, 20C20.
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Keywords: Lie group, Lie algebra, MD5-group, MD5-algebra, K-orbit, Foliation, Measured
foliation, C*-algebra, Connes' C*-algebra associated to a measured
foliation.
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