Associativity certificates for Kontsevich's star-product $\star$ mod $\bar{o}(\hbar^k)$: $k\leqslant 6$ unlike $k\geqslant7$
| Autor: | Buring, Ricardo, Kiselev, Arthemy V. |
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| Rok vydání: | 2023 |
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| Zdroj: | Journal of Physics: Conference Series, Vol.2667 (2023), Paper 012080, pp.1--8 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-6596/2667/1/012080 |
| Popis: | The formula $\star$ mod $\bar{o}(\hbar^k)$ of Kontsevich's star-product with harmonic propagators was known in full at $\hbar^{k\leqslant 6}$ since 2018 for generic Poisson brackets, and since 2022 also at $k=7$ for affine brackets. We discover that the mechanism of associativity for the star-product up to $\bar{o}(\hbar^6)$ is different from the mechanism at order $7$ for both the full star-product and the affine star-product. Namely, at lower orders the needed consequences of the Jacobi identity are immediately obtained from the associator mod $\bar{o}(\hbar^6)$, whereas at order $\hbar^7$ and higher, some of the necessary differential consequences are reached from the Kontsevich graphs in the associator in strictly more than one step. Comment: Expanded extract from arXiv:2209.14438 [q-alg]; Proc. international symposium on Quantum Theory and Symmetries (QTS12) on 24-28 July 2023 in CVUT Prague, Czech Republic; 8 pages + Appendices (7pp.), 2 tables, 1 figure |
| Databáze: | arXiv |
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