6533b86dfe1ef96bd12c9572

RESEARCH PRODUCT

Compressed Drinfeld associators

Vitaliy Kurlin

subject

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Hexagon equationPure mathematicsCampbell–Baker–Hausdorff formulaKnotLie algebraModuloCompressed Vassiliev invariantsPentagon equation01 natural sciencessymbols.namesakeMathematics - Geometric TopologyChord diagramsExtended Bernoulli numbers[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Mathematics::Quantum Algebra0103 physical sciencesLie algebraMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)0101 mathematicsAlgebraic numberBernoulli numberQuotientMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Zeta functionDiscrete mathematics[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA]Algebra and Number TheoryVassiliev invariants[ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]Drinfeld associator57M25 57M27 11B68 17B01010102 general mathematicsAssociatorQuantum algebraGeometric Topology (math.GT)Kontsevich integralRiemann zeta functionsymbols[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]Compressed associator010307 mathematical physicsBernoulli numbers

description

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.

yearjournalcountryeditionlanguage
2004-08-29
https://hal.archives-ouvertes.fr/hal-00013012