English

On the elliptic Kashiwara-Vergne Lie algebra

Quantum Algebra 2018-09-26 v1 Geometric Topology

Abstract

We recall the definitions of two independently defined elliptic versions of the Kashiwara-Vergne Lie algebra krv\frak{krv}, namely the Lie algebra krv(1,1)\frak{krv}^{(1,1)} constructed by A.Alekseev, N.Kawazumi, Y.Kuno and F.Naef arising from the study of graded formality isomorphisms associated to topological fundamental groups of surfaces, and the Lie algebra krvell\frak{krv}_{ell} defined using mould theoretic techniques arising from multiple zeta theory by E.Raphael and L.Schneps, and show that they coincide.

Keywords

Cite

@article{arxiv.1809.09340,
  title  = {On the elliptic Kashiwara-Vergne Lie algebra},
  author = {Elise Raphael and Leila Schneps},
  journal= {arXiv preprint arXiv:1809.09340},
  year   = {2018}
}