|
SIGMA 2 (2006), 080, 3 pages math.QA/0404262
https://doi.org/10.3842/SIGMA.2006.080
Contribution to the Vadim Kuznetsov Memorial Issue
A Formula for the Logarithm of the KZ Associator
Benjamin Enriquez a and Fabio Gavarini b
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
Received October 03, 2006, in final form November 10, 2006; Published online November 13, 2006
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).
Key words:
free Lie algebras; Campbell-Baker-Hausdorff series; Knizhnik-Zamolodchikov associator.
pdf (173 kb)
ps (143 kb)
tex (7 kb)
References
- Drinfeld V., On quasitriangular quasi-Hopf algebras
and a group closely connected with Gal(`Q/ Q),
Leningrad Math. J., 1991, V.2, 829-860.
- Enriquez B.,
Quasi-reflection algebras, multiple polylogarithms at roots of 1,
and analogues of the group GT, math.QA/0408035.
- Le T.T.Q., Murakami J., Kontsevich's integral for the
Kauffman polynomial, Nagoya Math. J., 1996, V.142, 39-65.
- Reutenauer C., Free Lie algebras,
London Mathematical Society Monographs. New Series, Vol. 7,
Oxford Science Publications, New York, The Clarendon Press,
Oxford University Press, 1993.
|
|