The cyclic theory of Hopf algebroids

Details The cyclic theory of Hopf algebroids The cyclic theory of Hopf algebroids

2009-04-30

arxiv.org/abs/0904.4736v2

Mathematics

K-Theory and Homology

44 pages; to appear in Journal of Noncommutative Geometry

Scientific paper

We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic object. We derive general structure theorems for these theories in the special cases of commutative and cocommutative Hopf algebroids. Finally, we compute the cyclic theory in examples associated to Lie-Rinehart algebras and \'etale groupoids.

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