Abstract :
We construct a functorial filtration on the integral homology of an abelian group B, for which the associated graded pieces are the values at B of the left derived functors LiΛj( ,0) of the exterior algebra functors Λj. It is shown that LiΛj(B,0) is isomorphic to the group of elements in image which are anti-invariant under the natural action of the symmetric group Σj. A presentation is given for the groups Lj−1Λj(B,0), which are of particular interest, since they are natural generalizations of the group ΩB introduced by Eilenberg–Mac Lane [8]. This is illustrated by a functorial description of the integral homology in degrees ≤5 of an abelian group B, and sheds new light on the computations by Hamsher of Hi(B) for all i [12].
