#### 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.

Notes on file formats
Nathan Geer

School of Mathematics, Georgia Institute of Technology

Atlanta, GA 30332-0160, USA

Email: geer@math.gatech.edu

URL: www.math.gatech.edu/~geer/

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