Explicit Description of Compressed Logarithms of All Drinfeld Associators
نویسنده
چکیده
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]. We describe explicitly the images of the logarithms of all Drinfeld associators in a completion of the quotient L/ [ [L,L], [L,L] ] . The main ingredient of our proofs is an explicit form of Cambell-Baker-Hausdorff formula in the case when all commutators commute.
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