Home /  Workshop /  Schedules /  A stabilizer interpretation de double shuffle Lie algebras

A stabilizer interpretation de double shuffle Lie algebras

Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017

March 29, 2017 (10:30 AM PDT - 11:30 AM PDT)
Speaker(s): Benjamin Enriquez (Université de Strasbourg)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords
  • Galois theory

  • Galois orbits

  • Periods

  • Lie bialgebras

  • dmr and DMR

  • outer automorphisms

  • Grothendieck-Teichmuller group

  • shuffle product

  • harmonic coproduct

  • multiple zeta values

  • universal mapping properties

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Enriquez

Abstract

We recall the main results of double shuffle theory: the cyclotomicanalogues of MZVs (of order $N\geq 1$) satisfy a collection of relations arising from the study of their combinatorics, and also from their identifications with periods. The scheme arising from these relations is a torsor Under a prounipotent algebraic group $\mathrm{DMR}_0$.  This is a subgroup of the group $\mathrm{Out}^*$ of invariant tangential outer automorphisms of a free Lie algebra, equipped with an action of $\mu_N$. The Lie algebra $\mathfrak{dmr}_0$ of $\mathrm{DMR}_0$ is a subspace of the Lie algebra $\mathrm{out}^*$, defined by a pair of shuffle relations (Racinet) and containing the Grothendieck-Teichmüller Lie algebra or its analogues(Furusho). We show that the harmonic coproduct may be viewed as an element of a module over $\mathrm{out}^*$, and that $\mathfrak{dmr}_0$ then identifies with the stabilizer Lie algebra of this element. A similar identification concerning $\mathrm{DMR}_0$ enables one to construct a "Betti" version of the harmonic coproduct, and to identify the scheme arising from double shuffle relations as the set of elements of $\mathrm{Out}^*$ taking the harmonic coproduct to its "Betti" version

Supplements
28373?type=thumb Enriquez.Notes 626 KB application/pdf Download
Video/Audio Files

Enriquez

H.264 Video 10-Enriquez.mp4 562 MB video/mp4 rtsp://videos.msri.org/data/000/028/112/original/10-Enriquez.mp4 Download
Troubles with video?

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.