Cyclic Homology of Algebras

  • Jean-Louis Loday
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)


There are at least three ways to construct cyclic homology from Hochschild homology. First, in his search for a non-commutative analogue of de Rham homology theory, A. Connes discovered in 1981 the following striking phenomenon:
  • the Hochschild boundary map b is still well-defined when one factors out the module AA n = A n +1 by the action of the (signed) cyclic permutation of order n + 1.


Exact Sequence Mixed Complex Cyclic Module Cyclic Homology Hochschild Homology 
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Bibliographical Comments on Chapter 2

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jean-Louis Loday
    • 1
  1. 1.Centre National de la Recherche ScientifiqueInstitut de Recherche Mathématique AvancéeStrasbourgFrance

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