Volume 6, issue 2 (2002)

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Caractères sur l'algèbre de diagrammes trivalents Lambda

Bertrand Patureau-Mirand

Geometry & Topology 6 (2002) 563–607
 arXiv: math.GT/0107137
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.

Keywords
finite type invariants, weight system, representation theory
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25 17B10