2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137479We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial characterization of this algebra is given. Differentiability properties of the star product underlying the Kauffman bracket are discussed.22 pages. In this version we correct some typographical mistakes and improve the exposition in a few placesGeometric TopologyQuantum Algebra57M25, 57M35, 57R42text