{"title":"Poisson brackets and coaction maps of regularized holonomies of the KZ equation","authors":"Anton Alekseev, Florian Naef, Muze Ren","doi":"arxiv-2409.08894","DOIUrl":null,"url":null,"abstract":"We derive explicit closed formulas for the Kirillov-Kostant-Souriau (KKS)\ncoaction maps of open path regularized holonomies of the Knizhnik-Zamolodchikov\n(KZ) equation, and the corresponding Poisson brackets for the Lie algebra ${\\rm\ngl}(N, \\mathbb{C})$. Our main technical tool is a certain projection of the\ngeneralized pentagon equation of \\cite{AFR2024}.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Quantum Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08894","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We derive explicit closed formulas for the Kirillov-Kostant-Souriau (KKS)
coaction maps of open path regularized holonomies of the Knizhnik-Zamolodchikov
(KZ) equation, and the corresponding Poisson brackets for the Lie algebra ${\rm
gl}(N, \mathbb{C})$. Our main technical tool is a certain projection of the
generalized pentagon equation of \cite{AFR2024}.
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