Résumé
We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of sl(2) using purely combinatorial methods based on Temperley-Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten-Reshetikhin-Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.