Cyclic homology and path algebra resolutions

Abstract

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.