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Cyclic homology and path algebra resolutions

Published online by Cambridge University Press:  24 October 2008

Dave Benson
Dave Benson
Affiliation:
Mathematical Institute, Oxford
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Extract

It follows from a theorem of Loday and Quillen (proposition 5·4 of [6]) that one may calculate the cyclic homology of an algebra in characteristic zero by taking a semisimplicial resolution by free algebras, quotienting out commutators and then taking homology of the resulting complex. In this paper we explain how this is a special case of a more general method based on resolutions by path algebras of directed graphs. The Loday–Quillen result may be seen as the case where the graph has only one vertex.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 57 - 66
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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