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arXiv · 1011.3471

Cyclic structures in algebraic (co)homology theories

Niels Kowalzig·Ulrich Kraehmer
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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.

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Niels Kowalzig, Ulrich Kraehmer. 2010-11-15. Cyclic structures in algebraic (co)homology theories. https://arxiv.org/abs/1011.3471

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