Construction of Lie algebra weight system kernel via Vogel algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910793914646528 |
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| author | Khudoteplov, Dmitry Lanina, Elena Sleptsov, Alexey |
| author_facet | Khudoteplov, Dmitry Lanina, Elena Sleptsov, Alexey |
| contents | We develop a method of constructing a kernel of Lie algebra weight system. A main tool we use in the analysis is Vogel's $Λ$ algebra and the surrounding framework. As an example of a developed technique we explicitly provide all Jacobi diagrams lying in the kernel of $\mathfrak{sl}_N$ weight system at low orders. We also discuss consequences of the presence of the kernel in Lie algebra weight systems for detection of correlators in the 3D Chern-Simons topological field theory and for distinguishing of knots by the corresponding quantum knot invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of Lie algebra weight system kernel via Vogel algebra Khudoteplov, Dmitry Lanina, Elena Sleptsov, Alexey Quantum Algebra High Energy Physics - Theory Mathematical Physics Geometric Topology Representation Theory We develop a method of constructing a kernel of Lie algebra weight system. A main tool we use in the analysis is Vogel's $Λ$ algebra and the surrounding framework. As an example of a developed technique we explicitly provide all Jacobi diagrams lying in the kernel of $\mathfrak{sl}_N$ weight system at low orders. We also discuss consequences of the presence of the kernel in Lie algebra weight systems for detection of correlators in the 3D Chern-Simons topological field theory and for distinguishing of knots by the corresponding quantum knot invariants. |
| title | Construction of Lie algebra weight system kernel via Vogel algebra |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2411.14417 |