Year: 2014
Type: preprint
Abstract: We construct a family of Drinfeld associators interpolating between the Knizhnik-Zamolodchikov associator, the Alekseev-Torossian associator and the anti-Knizhnik-Zamolodchikov associator. We give explicit integral formulæ for the family of elements of the Grothendieck-Teichmüller Lie algebra tangent to the family of associators. As an application, we settle a conjecture of Pavel Etingof about the Alekseev-Torossian associator. Furthermore, we give explicit integral formulæ for the family of stable formality morphisms corresponding (in a precise way) to the above family of associators, and for the family of graph cohomology classes corresponding to the above family of elements of the Grothendieck-Teichmüller Lie algebra. It follows in particular that the ``logarithmic'' Kontsevich formality morphism corresponds to the Knizhnik-Zamolodchikov associator.
Source: arXiv (Cornell University)
Authors: Rossi, Carlo A., Willwacher, Thomas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W209040407