Compressed Drinfeld associators

JOURNAL OF ALGEBRA

卷:292

Article

Kurlin, V

关键词: Drinfeld associator;    compressed associator;    Kontsevich integral;    zeta function;    knot;    hexagon equation;    pentagon equation;    Bernoulli numbers;    extended Bernoulli numbers;    Campbell-Baker-Hausdorff formula;    Lie algebra;    chord diagrams;    Vassiliev invariants;    compressed Vassiliev invariants;   

DOI  :  10.1016/j.jalgebra.2005.05.013

来源: Elsevier

【 摘 要 】

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. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free