Algebraic & Geometric Topology 5 (2005) 1111–1139

DOI: 10.2140/agt.2005.5.1111

arXiv: math.GT/0411053

Abstract

Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: (1) quantum group invariants using the R–matrix, (2) the Kontsevich universal link invariant followed by the Lie algebra based weight system. Le and Murakami showed that these two link invariants are the same. These constructions can be generalized to some classes of Lie superalgebras. In this paper we show that constructions (1) and (2) give the same invariants for the Lie superalgebras of type A–G. We use this result to investigate the Links–Gould invariant. We also give a positive answer to a conjecture of Patureau-Mirand's concerning invariants arising from the Lie superalgebra D(2,1;α).

Keywords

Vassiliev invariants, weight system, Kontsevich integral, Lie superalgebras, Links–Gould invariant, quantum invariants

Mathematical Subject Classification

Primary: 57M27

Secondary: 17B37, 17B65

References

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Publication

Received: 6 May 2005
Accepted: 15 August 2005
Published: 11 September 2005

Authors