Algebraic and Geometric Topology 5 (2005), paper no. 45, pages 1111-1139.

The Kontsevich integral and quantized Lie superalgebras

Nathan Geer

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;alpha).

Keywords. Vassiliev invariants, weight system, Kontsevich integral, Lie superalgebras, Links-Gould invariant, quantum invariants

AMS subject classification. Primary: 57M27. Secondary: 17B65, 17B37.

E-print: arXiv:math.GT/0411053

DOI: 10.2140/agt.2005.5.1111

Submitted: 6 May 2005. Accepted: 15 August 2005. Published: 11 September 2005.

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Nathan Geer
School of Mathematics, Georgia Institute of Technology
Atlanta, GA 30332-0160, USA

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