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Foliations Formed by Generic Coadjoint Orbits of Lie Groups Corresponding to a Class Seven-Dimensional Solvable Lie Algebras (2208.06116v4)
Published 12 Aug 2022 in math.DG
Abstract: We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s {X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5}$ of Dixmier. First, we give a geometric description 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.