Title: Foliations formed by generic coadjoint orbits of a class of 7-dimensional solvable Lie groups
Abstract: Abstract We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical g 5,2 = span{X 1 , X 2 , X 3 , X 4 , X 5 : [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.