DETERMINING LIE ALGEBRA OF TRANSVERSE FOLIATED VECTOR FIELD OF THE EXTENSION OF DENSE LEAF LIE FOLIATION ON A COMPACT CONNECTED MANIFOLD

International audienceIn [1, 2], we showed that any extension of a Lie -foliation having dense leaves on a compact connected manifold M corresponds to a Lie subalgebra of In this paper, we determine the Lie algebra of -transverse foliated vector fields of an extension corresponding to the subalgebra Noting by the -transverse foliated vector field associated to we prove tha