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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.

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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