On ranks of the stable derivation algebra and Deligne's problem
type: Item
instance of: scholarly article
title: On ranks of the stable derivation algebra and Deligne's problem
zbMATH Open document ID: 0922.11093
author: Hiroshi Tsunogai
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-10-04T00:00:00Z
review text: The author reports some computational results on Deligne's problem on the estimation of the Galois image in the pro-\(l\) fundamental group of the projective line minus three points. The problem is to compare certain two graded Lie algebras, one comes from the above Galois representation and the other is Ihara's stable derivation algebra [\textit{Y. Ihara}, Isr. J. Math. 80, 135-153 (1992; Zbl 0782.20034)] linearizing the Grothendieck-Teichmüller group. Over the \(l\)-adic rationals, these two are conjectured to be equal and freely generated by the Ihara-Soulé elements in degrees \(2k+1\) \((k=1,2,\dots)\). The author reports that this conjecture is valid up to degree 12 and that certain iterated brackets of the Ihara-Soulé elements in degrees up to 17 are linearly independent as expected by the conjecture. The method uses previous studies by \textit{Y. Ihara} and \textit{M. Matsumoto} [Contemp. Math. 186, 201-213 (1995; Zbl 0848.11057)] and the author himself [Publ. Res. Inst. Math. Sci. 31, 113-134 (1995; Zbl 0838.11040)]. The updated web-site providing the computer program used in the study is located at ftp://tnt.math.metro-u.ac.jp/pub/program/lie-1.0.tar.gz.
reviewed by: Hiroaki Nakamura
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 20F40
zbMATH DE Number: 1022289
zbMATH Keywords: stable derivation algebra
zbMATH Keywords: Grothendieck-Teichmüller group
zbMATH Keywords: pro-\(l\) fundamental group
zbMATH Keywords: free Lie algebra
zbMATH Keywords: Hall basis
zbMATH Keywords: Ihara-Soulé elements
MaRDI profile type: Publication
full work available at URL: pjaa.73.29
OpenAlex ID: W2036208030
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DOI: 10.3792/PJAA.73.29
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description: scientific article; zbMATH DE number 1022289