2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63755We construct real polarizable Hodge structures on the reduced leafwise cohomology of Kähler-Riemann foliations by complex manifolds. As in the classical case one obtains a hard Lefschetz theorem for this cohomology. Serre's Kählerian analogue of the Weil conjectures carries over as well. Generalizing a construction of Looijenga and Lunts one obtains possibly infinite dimensional Lie algebras attached to Kähler-Riemann foliations. Finally using $(\mathfrak{g},K)$-cohomology we discuss a class of examples obtained by dividing a product of symmetric spaces by a cocompact lattice and considering the foliations coming from the factors.to appear in Annals of Global Analysis and GeometryDifferential GeometryComplex VariablesK-Theory and Homology37F75; 53C12; 58A14text