2023 Measurable Foliations Associated to the Coadjoint Representation of a Class of Seven-Dimensional Solvable Lie Groups
Vu Le, Tuyen Nguyen, Tuan Nguyen
J. Geom. Symmetry Phys. 65: 41-65 (2023). DOI: 10.7546/jgsp-65-2023-41-65

Abstract

We consider connected and simply connected seven-dimensional Lie groups whose Lie algebras have nilradical ${\frak g}_{5,2}$ 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.

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Vu Le. Tuyen Nguyen. Tuan Nguyen. "Measurable Foliations Associated to the Coadjoint Representation of a Class of Seven-Dimensional Solvable Lie Groups." J. Geom. Symmetry Phys. 65 41 - 65, 2023. https://doi.org/10.7546/jgsp-65-2023-41-65

Information

Published: 2023
First available in Project Euclid: 23 May 2023

Digital Object Identifier: 10.7546/jgsp-65-2023-41-65

Rights: Copyright © 2023 Bulgarian Academy of Sciences, Institute of Mechanics

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