More about the (co)homology of groups and associative algebras

It is proved that the homology and cohomology theories of groups and associative algebras are non-abelian derived functors of the cokernel and kernel groups of higher dimensions of their defining standard chain and cochain complexes respectively. The same results are also obtained for the relative (...

Full description

Saved in:
Bibliographic Details
Published in:Homology, homotopy, and applications homotopy, and applications, 2005, Vol.7 (1), p.87-108
Main Author: Inassaridze, Hvedri
Format: Article
Language:English
Subjects:
18G10
18G25
18G50
18G55
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is proved that the homology and cohomology theories of groups and associative algebras are non-abelian derived functors of the cokernel and kernel groups of higher dimensions of their defining standard chain and cochain complexes respectively. The same results are also obtained for the relative (co)homology of groups, the mod q cohomology of groups and the cohomology of groups with operators. This allowed us to give an alternative approach to higher Hopf formulas for integral homology of groups. An axiomatic characterization of the relative cohomology of groups is given and higher relative (n+1)-th cohomology of groups is described in terms of n-fold extensions.
ISSN:1532-0073
1532-0081
DOI:10.4310/HHA.2005.v7.n1.a6