# Les isomorphismes infinit\'esimaux des tissus de codimension 1

## TL;DR

This paper classifies the Lie algebras of infinitesimal symmetries of codimension 1 webs on manifolds, showing they are direct products of specific Lie algebras and providing bounds and examples.

## Contribution

It provides a complete description of the possible Lie algebras of infinitesimal diffeomorphisms for these webs, including their structure and limitations.

## Key findings

- Lie algebras are direct products of rak{sl}(2), non-commutative 2D, or commutative algebras
- Bound on the number of direct factors in the Lie algebra
- Constructed examples illustrating the classification

## 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.