2004/08/29 by V. Kurlin, Kurlin, V.
Mathematics · #11B68 #17B01 #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:11B68 #msc:17B01 #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.math/0408398
36 pages, 5 figures
arxiv created 2004/10/18 · arxiv updated 2009/12/01
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 algbera 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 satisfy 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.