A Formula for the Logarithm of the KZ Associator

Details A Formula for the Logarithm of the KZ Associator A Formula for the Logarithm of the KZ Associator

2004-04-14

arxiv.org/abs/math/0404262v2

SIGMA 2 (2006), 080, 3 pages

Mathematics

Quantum Algebra

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2006.080

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).

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