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The logarithmic star product in the linear case and the Grothendieck--Teichmüller group

2012/05/22 by Carlo A. Rossi, Rossi, Carlo A.
Mathematics · #17B35 #81R60 #Analytic and geometric function theory #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #Quantum Algebra (math.QA) #math.QA #msc:17B35 #msc:81R60

paper · pdf · doi:10.48550/arxiv.1205.4942

The paper has been withdrawn, because I have posted it wrongly the first time on the arXiv. Then, I decided to change the title radically and added some more technical details

openalex publication_date 2012/05/22 · arxiv created 2012/06/09 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this short note is to establish an explicit equivalence between two star products ⋆ and ⋆log on the symmetric algebra \mathrm S(\mathfrak g) of a finite-dimensional Lie algebra \mathfrak g over a field \mathbb K⊃\mathbb C of characteristic 0: the differential operator of infinite order with constant coefficients realizing the equivalence is related to the Grothendieck-Teichmüller group.

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