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Symmetric cohomology of groups

Symmetric cohomology of groups
Symmetric cohomology of groups

We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We show in particular, that there is a map from exterior cohomology to symmetric cohomology which is a split monomorphism in general and an isomorphism in many cases, but not always. We introduce two spectral sequences which help to explain the relationship between these cohomology groups. As a sample application we obtain that symmetric and classical cohomologies are isomorphic for torsion free groups.

Exterior algebra, Group cohomology, Spectral sequences
0021-8693
397-418
Pirashvili, Mariam
74a0b0b2-acbd-4ee2-9825-d8418ef74b5d
Pirashvili, Mariam
74a0b0b2-acbd-4ee2-9825-d8418ef74b5d

Pirashvili, Mariam (2018) Symmetric cohomology of groups. Journal of Algebra, 509, 397-418. (doi:10.1016/j.jalgebra.2018.05.020).

Record type: Article

Abstract

We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We show in particular, that there is a map from exterior cohomology to symmetric cohomology which is a split monomorphism in general and an isomorphism in many cases, but not always. We introduce two spectral sequences which help to explain the relationship between these cohomology groups. As a sample application we obtain that symmetric and classical cohomologies are isomorphic for torsion free groups.

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More information

Accepted/In Press date: 24 May 2018
e-pub ahead of print date: 1 June 2018
Published date: 1 September 2018
Keywords: Exterior algebra, Group cohomology, Spectral sequences

Identifiers

Local EPrints ID: 421898
URI: http://eprints.soton.ac.uk/id/eprint/421898
DOI: doi:10.1016/j.jalgebra.2018.05.020
ISSN: 0021-8693
PURE UUID: 1bba1de4-050c-4132-9fe6-291fb54472bb

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Date deposited: 06 Jul 2018 16:30
Last modified: 18 Mar 2024 05:18

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Author: Mariam Pirashvili

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