The multiple zeta value algebra and the stable derivation algebra
type: Item
instance of: scholarly article
title: The multiple zeta value algebra and the stable derivation algebra
zbMATH Open document ID: 1115.11055
author: Hidekazu Furusho
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2004-11-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.prims/1145476044
review text: Summary: The MZV algebra is the graded algebra over \(\mathbb Q\) generated by all multiple zeta values. The stable derivation algebra is a graded Lie algebra version of the Grothendieck-Teichmüller group. We shall show that there is a canonical surjective \(\mathbb Q\)-linear map from the graded dual vector space of the stable derivation algebra over \(\mathbb Q\) to the new-zeta space, the quotient space of the sub-vector space of the MZV algebra whose grade is greater than 2 by the square of the maximal ideal. As a corollary, we get an upper bound for the dimension of the graded piece of the MZV algebra at each weight in terms of the corresponding dimension of the graded piece of the stable derivation algebra. If some standard conjectures by Y. Ihara and P. Deligne concerning the structure of the stable derivation algebra hold, this will become a bound conjectured in Zagier's talk at the first European Congress of Mathematics. Via the stable derivation algebra, we can compare the new-zeta space with the \(l\)-adic Galois image Lie algebra which is associated with the Galois representation on the pro-\(l\) fundamental group of \(\mathbb P^1_{\overline{\mathbb Q}}-\{0,1,\infty\}\).
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 14G32
zbMATH DE Number: 2113011
MaRDI profile type: Publication
OpenAlex ID: W2052728736
cites work: Q4196514
cites work: Q3977509
DOI: 10.2977/PRIMS/1145476044
description: scientific article; zbMATH DE number 2113011