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

Ricardo Buring; Arthemy V. Kiselev

doi:10.1088/1742-6596/2667/1/012080

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

Ricardo Buring, Arthemy V. Kiselev^*

^*Corresponding author for this work

Algebra

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-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 language	English
Title of host publication	XII International Symposium on Quantum Theory and Symmetries (QTS12)
Publisher	IoP Publishing
Number of pages	9
DOIs	https://doi.org/10.1088/1742-6596/2667/1/012080
Publication status	Published - 2023
Event	12th International Symposium on Quantum Theory and Symmetries, QTS 2023 - Prague, Czech Republic Duration: 24-Jul-2023 → 28-Jul-2023

Publication series

Name	Journal of Physics: Conference Series
Publisher	IoP Publishing
Number	1
Volume	2667
ISSN (Print)	1742-6588

Conference

Conference	12th International Symposium on Quantum Theory and Symmetries, QTS 2023
Country/Territory	Czech Republic
City	Prague
Period	24/07/2023 → 28/07/2023

Access to Document

10.1088/1742-6596/2667/1/012080Licence: CC BY

Associativity certificates for Kontsevich’s star-product ? mod o¯(~ k ): k 6 6 unlike k > 7Final publisher's version, 920 KBLicence: CC BY

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

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.",

author = "Ricardo Buring and Kiselev, {Arthemy V.}",

note = "Publisher Copyright: {\textcopyright} Published under licence by IOP Publishing Ltd.; 12th International Symposium on Quantum Theory and Symmetries, QTS 2023 ; Conference date: 24-07-2023 Through 28-07-2023",

year = "2023",

doi = "10.1088/1742-6596/2667/1/012080",

language = "English",

series = "Journal of Physics: Conference Series",

publisher = "IoP Publishing",

number = "1",

booktitle = "XII International Symposium on Quantum Theory and Symmetries (QTS12)",

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Buring, R & Kiselev, AV 2023, Associativity certificates for Kontsevich's star-product ∗ mod ō(h^k): K ≤ 6 unlike k ≥ 7. in XII International Symposium on Quantum Theory and Symmetries (QTS12). Journal of Physics: Conference Series, no. 1, vol. 2667, IoP Publishing, 12th International Symposium on Quantum Theory and Symmetries, QTS 2023, Prague, Czech Republic, 24/07/2023. https://doi.org/10.1088/1742-6596/2667/1/012080

Associativity certificates for Kontsevich's star-product ∗ mod ō(h^k): K ≤ 6 unlike k ≥ 7. / Buring, Ricardo; Kiselev, Arthemy V.
XII International Symposium on Quantum Theory and Symmetries (QTS12). IoP Publishing, 2023. (Journal of Physics: Conference Series; Vol. 2667, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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