The cyclic theory of Hopf algebroids

  • Niels Kowalzig

    Utrecht University
  • Hessel Posthuma

    Korteweg-de Vries Institute for Mathematics, Amsterdam


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 étale groupoids.

Cite this article

Niels Kowalzig, Hessel Posthuma, The cyclic theory of Hopf algebroids. J. Noncommut. Geom. 5 (2011), no. 3, pp. 423–476

DOI 10.4171/JNCG/82