Caractères sur l'algèbre de diagrammes trivalents Lambda

Abstract

The theory of Vassiliev invariants deals with many modules of diagrams on which the algebra $\Lambda$ defined by Pierre Vogel acts. By specifying a quadratic simple Lie superalgebra, one obtains a character on $\Lambda$. We show the coherence of these characters by building a map of graded algebras beetwen $\Lambda$ and a quotient of a ring of polynomials in three variables; all the characters induced by simple Lie superalgebras factor through this map. In particular, we show that the characters for the Lie superalgebra $\mathfrak{f}\left(4\right)$ with dimension 40 and for ${\mathfrak{s}\mathfrak{l}}_3$ are the same.