Generators for AutG, G free nilpotent

Andreadakis, S.

doi:10.1007/bf01246117

Cited by 11 publications

(4 citation statements)

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“…We remark that in 1984, Andreadakis [2] showed that Aut N n,k is generated by P , Q, S, U and k − 2 other elements for n ≥ k ≥ 2. No presentation for Aut N n,k is known except for Aut N 2,k for k = 1, 2 and 3 due to Lin [34].…”

Section: Twisted Cohomology Groupsmentioning

confidence: 95%

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A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

Satoh

2016

IRMA Lectures in Mathematics and Theoretical Physics

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Section: Twisted Cohomology Groupsmentioning

confidence: 95%

“…Andreadakis [1] calculated the images of the Magnus generators of IA n by the first Johnson homomorphism as 2) and showed that τ 1 is surjective.…”

Section: τmentioning

confidence: 99%

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

Satoh

2016

IRMA Lectures in Mathematics and Theoretical Physics

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“…For k ≥ 3, Goryaga [15] showed that Aut N n,k is finitely generated for n ≥ 3 · 2 k−2 + k and k ≥ 2. In 1984, Andreadakis [2] showed that Aut N n,k is generated by P , Q, S, U and the other k − 2 elements for n ≥ k ≥ 2. In this paper, we use the following Bryant and Gupta's result.…”

Section: Automorphism Group Of a Free Nilpotent Groupmentioning

confidence: 99%

On the derivation algebra of the free Lie algebra and trace maps

Enomoto

Satoh

2011

Algebr. Geom. Topol.

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2861On the derivation algebra of the free Lie algebra and trace maps NAOYA ENOMOTO TAKAO SATOHWe mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps. To begin with, we give the irreducible decomposition of the derivation algebra as a GL.n; Q/-module via the Schur-Weyl duality and some tensor product theorems for GL.n; Q/. Using them, we calculate the irreducible decomposition of the images of the Johnson homomorphisms of the automorphism group of a free group and a free metabelian group.Next, we consider some applications of trace maps: Morita's trace map and the trace map for the exterior product of H . First, we determine the abelianization of the derivation algebra of the Chen Lie algebra as a Lie algebra, and show that the abelianization is given by the degree one part and Morita's trace maps. Second, we consider twisted cohomology groups of the automorphism group of a free nilpotent group. In particular, we show that the trace map for the exterior product of H defines a nontrivial twisted second cohomology class of it.

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“…Using the tame automorphism, it is routine to verify that Andreadakis [5], reduced the restriction on n by proving that the same conclusion holds for n/> I. C. K. Gupta and Bryant [31] eliminated all but one ®k by proving that if n >~ l Aut F., l = (T.,~, 03).…”

Section: Automorphisms Of Solvable Groupsmentioning

confidence: 99%