University of Sydney Algebra Seminar
Zsuzsanna Dancso
Friday 17 May, 12-1pm, Place: SMRI seminar room (Macleay Building (A12) room 301)
Kashiwara-Vergne solutions degree by degree
The Kashiwara–Vergne (KV) problem was originally posed in the context of convolutions on Lie groups in 1978, and has wide implications from Lie theory to harmonic analysis. The first general solution was found in 2006, by Alekseev and Meinrenken. Later, Alekseev–Torossian reformulated the problem as a set of two equations for automorphisms of the degree completed free Lie algebra on two generators. In this talk we will introduce the Alekseev-Torossian formulation of the KV equations, and show that solutions can always be extended degree by degree, hence found recursively to higher and higher precision. This may be used to simplify the computation of a class of Drinfel’d associators, which conjecturally comprises all associators.
This is a report on some of the work I did while on sabbatical last semester, and is joint with Iva Halacheva, Guillaume Laplante-Anfossi and Marcy Robertson. The preprint is at https://arxiv.org/pdf/2310.20420.