Vitaliy Kurlin (University of Liverpool)
http://www.geocities.com/vak26
vitaliy.kurlin@liv.ac.uk 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.
Based on paper that has been recently published in Journal of Algebra, Volume 292, Issue 1, 1 October 2005, Pages 184-242, available online at http://authors.elsevier.com/sd/article/S0021869305003121 and also on my home page www.geocities.com/vak26.