Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-16T12:03:02.168Z Has data issue: false hasContentIssue false
  • English
  • Français

Cyclic homology and path algebra resolutions

Published online by Cambridge University Press:  24 October 2008

Dave Benson
Dave Benson
Affiliation:
Mathematical Institute, Oxford
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bass, H.. Algebraic K-theory (Benjamin Inc., 1968).Google Scholar
[2]Dold, A. and Puppe, D.. Homologie nicht-additiver Funktoren. Anwendungen. Ann. Inst. Fourier (Grenoble) 11 (1961), 201–312.CrossRefGoogle Scholar
[3]Dlab, V. and Ringel, C. M.. The representations of tame hereditary algebras. In Representation Theory of Algebras (Marcel Dekker, 1978), pp. 329–353.Google Scholar
[4]Gabriel, P.. Auslander-Reiten sequences and representation-finite algebras. In Representation theory I, Ottawa 1979, Lecture Notes in Math. vol. 831 (Springer-Verlag, 1980), pp. 1–71.Google Scholar
[5]Kassel, C.. L'homologie cyclique des algèbres enveloppantes. Invent. Math. 91 (1988), 221–251.CrossRefGoogle Scholar
[6]Loday, J.-L. and Quillen, D.. Cyclic homology and the Lie algebra homology of matrices. Comment. Math. Helv. 59 (1984), 565–591.CrossRefGoogle Scholar
[7]May, J. P.. Simplicial Objects in Algebraic Topology (University of Chicago Press, 1967).Google Scholar