Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909973777219584 |
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| author | Brown, Mollie S. Jagoe Kiselev, Arthemy V. |
| author_facet | Brown, Mollie S. Jagoe Kiselev, Arthemy V. |
| contents | Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensional affine manifolds. The calculus of Kontsevich graphs can be made dimension-specific for the class of Nambu--Poisson brackets given by Jacobian determinants. Using the Kontsevich--Nambu micro-graphs in dimensions $d\geqslant 2$, we explore the open problem of (non)triviality for Kontsevich's tetrahedral graph cocycle action on the space of Nambu--Poisson brackets. We detect a conjecturally infinite new set of differential-polynomial identities for Jacobian determinants of arbitrary sizes $d\times d$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems Brown, Mollie S. Jagoe Kiselev, Arthemy V. Combinatorics Quantum Algebra Symplectic Geometry 05C31, 05C90, 18G85, 53D55, 68R10 Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensional affine manifolds. The calculus of Kontsevich graphs can be made dimension-specific for the class of Nambu--Poisson brackets given by Jacobian determinants. Using the Kontsevich--Nambu micro-graphs in dimensions $d\geqslant 2$, we explore the open problem of (non)triviality for Kontsevich's tetrahedral graph cocycle action on the space of Nambu--Poisson brackets. We detect a conjecturally infinite new set of differential-polynomial identities for Jacobian determinants of arbitrary sizes $d\times d$. |
| title | Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems |
| topic | Combinatorics Quantum Algebra Symplectic Geometry 05C31, 05C90, 18G85, 53D55, 68R10 |
| url | https://arxiv.org/abs/2511.06121 |