We prove that the Lie algebra of infinitesimal automorphisms of the transverse structure on the total space of the transverse bundle of a foliation is isomorphic to the semi-direct product of the Lie algebra of the infinitesimal automorphism of the foliation by the vector space of the transverse vector fields. The derivations of this algebra are entirely determined and we prove that this Lie algebra characterises the foliated structure of a compact Hausdorff foliation.
@article{urn:eudml:doc:42245,
title = {Une caract\'erisation du fibr\'e transverse.},
journal = {Collectanea Mathematica},
volume = {41},
year = {1990},
pages = {35-44},
zbl = {0737.57014},
mrnumber = {MR1134444},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42245}
}
Van Duc, Tong. Une caractérisation du fibré transverse.. Collectanea Mathematica, Tome 41 (1990) pp. 35-44. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42245/