Associativity certificates for Kontsevich's star-product ∗ mod ō(hk ): K ≤ 6 unlike k ≥ 7

Ricardo Buring, Arthemy V. Kiselev*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Abstract

The formula ∗ mod ō(h k ) of Kontsevich's star-product with harmonic propagators was known in full ath k≥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 ō(h6) 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 ō(h6), whereas at orderh7 and higher, some of the necessary differential consequences are reached from the Kontsevich graphs in the associator in strictly more than one step.

Original languageEnglish
Title of host publicationXII International Symposium on Quantum Theory and Symmetries (QTS12)
PublisherIoP Publishing
Number of pages9
DOIs
Publication statusPublished - 2023
Event12th International Symposium on Quantum Theory and Symmetries, QTS 2023 - Prague, Czech Republic
Duration: 24-Jul-202328-Jul-2023

Publication series

NameJournal of Physics: Conference Series
PublisherIoP Publishing
Number1
Volume2667
ISSN (Print)1742-6588

Conference

Conference12th International Symposium on Quantum Theory and Symmetries, QTS 2023
Country/TerritoryCzech Republic
CityPrague
Period24/07/202328/07/2023

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