Kurlin, V. (2005) 'Compressed Drinfeld associators.', Journal of algebra., 292 (1). pp. 184-242.
Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations—hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algebra L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that obey the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell–Baker–Hausdorff formula in the case when all commutators commute.
|Keywords:||Drinfeld associator, Kontsevich integral, Zeta function, Knot, Bernoulli numbers, Campbell-Baker-Hausdorff formula, Lie algebra, Vassiliev invariants.|
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|Publisher Web site:||http://dx.doi.org/10.1016/j.jalgebra.2005.05.013|
|Record Created:||21 Sep 2007|
|Last Modified:||08 Apr 2010 16:37|
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