Compressed Drinfeld associators

Details Compressed Drinfeld associators Compressed Drinfeld associators

2004-08-29

arxiv.org/abs/math/0408398v2

Mathematics

Geometric Topology

36 pages, 5 figures

Scientific paper

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.

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