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The number of primitive Vassiliev invariants up to degree 12

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arxiv q-alg/9706022 v1 pith:CVNLC7ZZ submitted 1997-06-18 q-alg math.QA

Jan A. Kneissler This is my paper · ORCID
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We present algorithms giving upper and lower bounds for the number of independent primitive rational Vassiliev invariants of degree m modulo those of degree m-1. The values have been calculated for the formerly unknown degrees m = 10, 11, 12. Upper and lower bounds coincide, which reveals that all Vassiliev invariants of degree smaller 13 are orientation insensitive and are coming from representations of Lie algebras so and gl. Furthermore, a conjecture of Vogel is falsified and it is shown that the \Lambda-module of connected trivalent diagrams (Chinese characters) is not free.

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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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