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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 080, 3 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.080 (Mi sigma108) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A Formula for the Logarithm of the KZ Associator

Benjamin Enriqueza, Fabio Gavarinib

a IRMA (CNRS), rue René Descartes, F-67084 Strasbourg, France
b Universitá degli Studi di Roma ''Tor Vergata'', Dipartimento di Matematica, Via della Ricerca Scientifica 1, I-00133 Rome, Italy
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DOI: https://doi.org/10.3842/SIGMA.2006.080
Abstract: We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik–Zamolodchikov (KZ) associator Φ to derive a formula for log⁡(Φ) in terms of MZV's (multiple zeta values).
Keywords: free Lie algebras; Campbell–Baker–Hausdorff series, Knizhnik–Zamolodchikov associator.
Received: October 3, 2006; in final form November 10, 2006; Published online November 13, 2006
Bibliographic databases:
Document Type: Article
MSC: 17B01; 81R50
Language: English
Citation: Benjamin Enriquez, Fabio Gavarini, “A Formula for the Logarithm of the KZ Associator”, SIGMA, 2 (2006), 080, 3 pp.
Citation in format AMSBIB
\Bibitem{EnrGav06}
\by Benjamin Enriquez, Fabio Gavarini
\paper A~Formula for the Logarithm of the KZ Associator
\jour SIGMA
\yr 2006
\vol 2
\papernumber 080
\totalpages 3
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\crossref{https://doi.org/10.3842/SIGMA.2006.080}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2264896}
\zmath{https://zbmath.org/?q=an:05236989}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889234803}
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    • This publication is cited in the following 2 articles:
    1. Alekseev A., Enriquez B., Torossian C., “Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations”, Publ. Math. Inst. Hautes Études Sci., 2010, no. 112, 143–189  crossref  mathscinet  zmath  isi  scopus
    2. Enriquez B., “Quasi-reflection algebras and cyclotomic associators”, Selecta Mathematica-New Series, 13:3 (2007), 391–463  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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