The cyclic theory of Hopf algebroids

By N. Kowalzig, H. Posthuma. 2009

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We give a systematic description of the cyclic cohomology theory of Hopf alge\-broids 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f3db0df02b6c7f6427585ee4fcca3a7b1191cc8