Les isomorphismes infinit\'esimaux des tissus de codimension 1

Abstract

We study local ($n+1$)-webs of codimension 1 on a manifold of dimension $n.$ We give a complete description of their possible Lie algebras of infinitesimal diffeomorphisms. More precisely we show that these Lie algebras are direct products of sub-algebras which are isomorphic to $\frak{sl}(2),$ to the non-commutative 2-dimensional Lie algebra or commutative. We give also a precise limitation of the number of such direct factors and examples.