A formula for the logarithm of the KZ associator

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2006
• ISSN: 1815-0659
• Main Authors: Enriquez, B., Gavarini, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146087
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A formula for the logarithm of the KZ associator / B. Enriquez, F. Gavarini // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 4 назв. — англ.

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)....