Cyclic cohomology of (extended) Hopf algebras

2003 ◽  
Author(s):  
M. Khalkhali ◽  
B. Rangipour
Keyword(s):  
Hopf Algebras ◽  
Cyclic Cohomology

On codihedral module for *-Hopf algebras

2008 ◽  
Vol 2 (2) ◽  
pp. 353-360
Author(s):  
Th. Yu. Popelensky
Keyword(s):  
Hopf Algebras ◽  
Cyclic Cohomology

AbstractWe construct dihedral and reflexive cohomology theories for *-Hopf algebras. This generalizes the Connes–Moscovici construction of cyclic cohomology for Hopf algebras.

scholarly journals Cyclic cohomology of Hopf algebras

2002 ◽  
Vol 166 (1-2) ◽  
pp. 29-66 ◽  
Author(s):  
Marius Crainic
Keyword(s):  
Hopf Algebras ◽  
Cyclic Cohomology

scholarly journals Cyclic cohomology and Baaj-Skandalis duality

2013 ◽  
Vol 13 (1) ◽  
pp. 115-145 ◽  
Author(s):  
Christian Voigt
Keyword(s):  
Quantum Group ◽  
Lie Groups ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Cyclic Homology ◽  
Cyclic Cohomology ◽  
Important Ingredient ◽  
Kasparov Theory

AbstractWe construct a duality isomorphism in equivariant periodic cyclic homology analogous to Baaj-Skandalis duality in equivariant Kasparov theory. As a consequence we obtain general versions of the Green-Julg theorem and the dual Green-Julg theorem in periodic cyclic theory.Throughout we work within the framework of bornological quantum groups, thus in particular incorporating at the same time actions of arbitrary classical Lie groups as well as actions of compact or discrete quantum groups. An important ingredient in the construction of our duality isomorphism is the notion of a modular pair for a bornological quantum group, closely related to the concept introduced by Connes and Moscovici in their work on cyclic cohomology for Hopf algebras.

scholarly journals On Cyclic Cohomology of ×-Hopf algebras

2014 ◽  
Vol 13 (1) ◽  
pp. 147-170
Author(s):  
Mohammad Hassanzadeh
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Cyclic Cohomology ◽  
Drinfeld Modules ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Algebraic Tori ◽  
Characteristic Map ◽  
Hopf Algebroids

AbstractIn this paper we study the cyclic cohomology of certain ×-Hopf algebras: universal enveloping algebras, quantum algebraic tori, the Connes-Moscovici ×-Hopf algebroids and the Kadison bialgebroids. Introducing their stable anti Yetter-Drinfeld modules and cocyclic modules, we compute their cyclic cohomology. Furthermore, we provide a pairing for the cyclic cohomology of ×-Hopf algebras which generalizes the Connes-Moscovici characteristic map to ×-Hopf algebras. This enables us to transfer the ×-Hopf algebra cyclic cocycles to algebra cyclic cocycles.

scholarly journals Cyclic cohomology of Hopf algebras of transverse symmetries in codimension 1

2007 ◽  
Vol 210 (1) ◽  
pp. 323-374 ◽  
Author(s):  
Henri Moscovici ◽  
Bahram Rangipour
Keyword(s):  
Hopf Algebras ◽  
Cyclic Cohomology
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