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The Kontsevich integral and quantized Lie superalgebras

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arxiv math/0411053 v2 pith:VDOVOSMV submitted 2004-11-02 math.GT

Nathan Geer This is my paper · ORCID
classification math.GT
keywords invariantslinksuperalgebrasalgebraconstructionsgiveinvariantkontsevich
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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 D(2,1;alpha).

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  1. Construction of Lie algebra weight system kernel via Vogel algebra

    math.QA 2024-11 conditional novelty 6.0 of 10

    Using Vogel's Lambda algebra, the authors construct and explicitly list the first Jacobi diagrams in the kernel of the sl_n weight system, up to order 10 for primitive diagrams.

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