# Cyclic structures in algebraic cohomology theories

Kowalzig, N. and Kraehmer, U. (2011) Cyclic structures in algebraic cohomology theories. Homology, Homotopy and Applications, 13(1), pp. 297-318.

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## Abstract

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.

Item Type: Articles Published Yes Kowalzig, Dr Niels and Kraehmer, Dr Ulrich College of Science and Engineering > School of Mathematics and Statistics > Mathematics Homology, Homotopy and Applications 1532-0073 arXiv

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