Caractères sur l’algèbre de diagrammes trivalents Lambda

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 ${s l}_{3}$ are the same.

Keywords

finite type invariants, weight system, representation theory

Mathematical Subject Classification 2000

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

Bertrand Patureau-Mirand
Centre de Recherche LMAM Université de Bretagne-Sud Campus de Tohannic BP 573 F-56017 Vannes France
http://www.univ-ubs.fr/lmam/patureau/

Volume 6, issue 2 (2002)

Bertrand Patureau-Mirand