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Abstract
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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
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Keywords
Vassiliev invariants, weight system, Kontsevich integral,
Lie superalgebras, Links–Gould invariant, quantum
invariants
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Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 17B65, 17B37
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Publication
Received: 6 May 2005
Accepted: 15 August 2005
Published: 11 September 2005
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