A Formula for the Logarithm of the KZ Associator

Benjamin Enriquez; Fabio Gavarini

doi:10.3842/SIGMA.2006.080

A Formula for the Logarithm of the KZ Associator

Quantum Algebra 2008-04-24 v2

Authors: Benjamin Enriquez , Fabio Gavarini

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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 $\Phi$ to derive a formula for $\log(\Phi)$ in terms of MZV's (multiple zeta values).

Keywords

kz associator logarithm free algebra group-like element multiple zeta values linear map

Cite

@article{arxiv.math/0404262,
  title  = {A Formula for the Logarithm of the KZ Associator},
  author = {Benjamin Enriquez and Fabio Gavarini},
  journal= {arXiv preprint arXiv:math/0404262},
  year   = {2008}
}

Comments

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

A Formula for the Logarithm of the KZ Associator

Abstract

Keywords

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