Geometry & Topology 6 (2002) 563–607

DOI: 10.2140/gt.2002.6.563

arXiv: math.GT/0107137

Abstract

The theory of Vassiliev invariants deals with many modules of diagrams on which the algebra Λ defined by Pierre Vogel acts. By specifying a quadratic simple Lie superalgebra, one obtains a character on Λ. We show the coherence of these characters by building a map of graded algebras beetwen Λ 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 f(4) with dimension 40 and for sl₃ are the same.

Keywords

finite type invariants, weight system, representation theory

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M25 17B10

References

Forward citations

Publication

Received: 4 July 2001
Accepted: 28 October 2002
Published: 1 December 2002
Proposed: Vaughan Jones
Seconded: Robion Kirby, Joan Birman

Authors