Compressed Drinfeld associators

Kurlin, V

Abstract

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.

Citation

Kurlin, V. (2005). Compressed Drinfeld associators. Journal of Algebra, 292(1), 184-242. https://doi.org/10.1016/j.jalgebra.2005.05.013

• Journal Article Type: Article
• Publication Date: Oct 1, 2005
• Deposit Date: Sep 21, 2007
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Electronic ISSN: 1090-266X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 292
• Issue: 1
• Pages: 184-242
• DOI: https://doi.org/10.1016/j.jalgebra.2005.05.013
• Keywords: Drinfeld associator, Kontsevich integral, Zeta function, Knot, Bernoulli numbers, Campbell-Baker-Hausdorff formula, Lie algebra, Vassiliev invariants.
• Public URL: https://durham-repository.worktribe.com/output/1534815