Characters on the trivalent diagram algebra \(\Lambda\) (Q1428380)

The theory of Vassiliev invariants deals with many weight systems defined on modules of diagrams. By specifying a quadratic simple Lie super algebra, one obtains such weight systems and they induce characters on an algebra \(\Lambda\) defined by \textit{P. Vogel} [Algebraic structures on modules of diagrams, Preprint Univ. Paris VII, (1995)]. This paper is the proof of a coherence result relating to the characters on \(\Lambda\) announced by the author in [C. R. Acad. Sci., Paris, Ser. I, Math. 329, No. 9, 803-806 (1999; Zbl 0964.57009)]: all the characters induced by simple Lie super algebras factor through a map of graded algebras between \(\Lambda\) and a quotient of a ring of polynomials in three variables.