Abstract
We study the derived functors of the components Z.A/ of the divided power algebra Z.A/ associated to an abelian group A , with special emphasis on the d D 4 case. While our results have applications both to representation theory and to algebraic topology, we illustrate them here by providing a new functorial description of certain integral homology groups of the Eilenberg–Mac Lane spaces K.A; n/ for A a free abelian group. In particular, we give a complete functorial description of the groups H .K.A; 3/IZ/ for such A .
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