We construct a wide class of finite W-algebras as truncations of Yangians. These truncations correspond to algebra homomorphisms and allow to construct the W-algebras as exchange algebras, the R-matrix being the Yangian's one. As an application, we classify all irreducible finite dimensionnal representations of these W-algebras and determine their center.

@inproceedings{BriotL,
title={- le - Vieux de Physique Th{\'e}orique RTT presentation of finite W - algebras},
author={Christophe Briot and {\'E}ric Ragoucy}
}