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On Vassiliev Invariants not Coming from Semisimple Lie Algebras

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arxiv q-alg/9706005 v2 pith:XQPVITTX submitted 1997-06-04 q-alg math.QA

Jens Lieberum This is my paper · ORCID
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We prove a refinement of Vogel's statement that the Vassiliev invariants of knots coming from semisimple Lie algebras do not generate all Vassiliev invariants. This refinement takes into account the second grading on Vassiliev invariants induced by cabling of knots. As an application we get an amelioration of the actually known lower bounds for the dimensions of the space of Vassiliev invariants.

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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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