THE p-ZASSENHAUS FILTRATION of A FREE PROFINITE GROUP and SHUFFLE RELATIONS

Ido Efrat

doi:10.1017/S1474748021000426

THE p-ZASSENHAUS FILTRATION of A FREE PROFINITE GROUP and SHUFFLE RELATIONS

Ido Efrat

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For a prime number p and a free profinite group S on the basis X, let, be the p-Zassenhaus filtration of S. For n$ ]]>, we give a word-combinatorial description of the cohomology group in terms of the shuffle algebra on X. We give a natural linear basis for this cohomology group, which is constructed by means of unitriangular representations arising from Lyndon words.

Original language	English
Pages (from-to)	961-983
Number of pages	23
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	22
Issue number	2
DOIs	https://doi.org/10.1017/S1474748021000426
State	Published - 29 Mar 2023

Keywords

Galois cohomology
Massey products
modular dimension subgroups
p-Zassenhaus filtration
shuffle algebra
shuffle relations

ASJC Scopus subject areas

General Mathematics

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10.1017/S1474748021000426

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abstract = "For a prime number p and a free profinite group S on the basis X, let, be the p-Zassenhaus filtration of S. For n$ ]]>, we give a word-combinatorial description of the cohomology group in terms of the shuffle algebra on X. We give a natural linear basis for this cohomology group, which is constructed by means of unitriangular representations arising from Lyndon words.",

keywords = "Galois cohomology, Massey products, modular dimension subgroups, p-Zassenhaus filtration, shuffle algebra, shuffle relations",

author = "Ido Efrat",

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N2 - For a prime number p and a free profinite group S on the basis X, let, be the p-Zassenhaus filtration of S. For n$ ]]>, we give a word-combinatorial description of the cohomology group in terms of the shuffle algebra on X. We give a natural linear basis for this cohomology group, which is constructed by means of unitriangular representations arising from Lyndon words.

AB - For a prime number p and a free profinite group S on the basis X, let, be the p-Zassenhaus filtration of S. For n$ ]]>, we give a word-combinatorial description of the cohomology group in terms of the shuffle algebra on X. We give a natural linear basis for this cohomology group, which is constructed by means of unitriangular representations arising from Lyndon words.

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KW - Massey products

KW - modular dimension subgroups

KW - p-Zassenhaus filtration

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KW - shuffle relations

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THE p-ZASSENHAUS FILTRATION of A FREE PROFINITE GROUP and SHUFFLE RELATIONS

Abstract

Keywords

ASJC Scopus subject areas

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