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A new chain complex for the homology of the Steenrod algebra

Published online by Cambridge University Press:  24 October 2008

William M. Singer
William M. Singer
Affiliation:
Fordham University, New York
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Extract

Let A be the Steenrod algebra over the field F2. For any graded A-module M we construct here a small chain complex of A-modules EM. This complex computes the homology of the Steenrod algebra with coefficients in M, in the sense that:

The complexes F2 ⊗AEM are comparable in size but slightly larger than those that arise from the Λ-algebra(4). We are motivated to introduce them because they can be used to prove an embedding theorem for the homology of the Steenrod algebra. In fact, we construct a functor K on the category of graded. A-modules, and using the complexes EM, prove that there is a natural, one-one map:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 279 - 292
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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