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 étale groupoids.
The cyclic theory of Hopf algebroids / Kowalzig, Niels; Posthuma, HESSEL BOUKE. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - STAMPA. - 5:3(2011), pp. 423-476. [10.4171/JNCG/82]
The cyclic theory of Hopf algebroids
KOWALZIG, NIELS;POSTHUMA, HESSEL BOUKE
2011
Abstract
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 étale groupoids.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
