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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 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 2000
Primary: 57M27
Secondary: 57M25 17B10
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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/