Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

Cyclic structures in algebraic (co)homology theories

Pages: 297 – 318

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n1.a12


Niels Kowalzig (Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France)

Ulrich Krähmer (School of Mathematics and Statistics, University of Glasgow, Scotland, United Kingdom)


This note discusses the cyclic cohomology of a left Hopf algebroid ($\times_A$-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A generalisation of cyclic duality that makes sense for arbitrary para-cyclic objects yields a dual homology theory. The twisted cyclic homology of an associative algebra provides an example of this dual theory that uses coefficients that are not necessarily stable anti Yetter-Drinfel'd modules


cyclic homology; Hopf algebroid; twisted cyclic homology; Lie-Rinehart algebra

2010 Mathematics Subject Classification

16E40, 16T05, 16T15, 19D55, 58B34

Published 12 July 2011