scholarly journals Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem

1998 ◽  
Vol 198 (1) ◽  
pp. 199-246 ◽  
Author(s):  
A. Connes ◽  
H. Moscovici
Keyword(s):  
Hopf Algebras ◽  
Index Theorem ◽  
Cyclic Cohomology ◽  
Transverse Index

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 The equivariant index theorem in entire cyclic cohomology

2008 ◽  
Vol 3 (2) ◽  
pp. 261-307 ◽  
Author(s):  
Denis Perrot
Keyword(s):  
Homology Class ◽  
Chern Character ◽  
Index Theorem ◽  
Complete Riemannian Manifold ◽  
Cyclic Cohomology ◽  
Convolution Algebra ◽  
Cup Product ◽  
Compactly Supported Functions ◽  
Assembly Map ◽  
Banach Completion

AbstractLet G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifold M, with compact quotient G\M. There is an assembly map which associates to any G-equivariant K-homology class on M, an element of the topological K-theory of a suitable Banach completion of the convolution algebra of continuous compactly supported functions on G. The aim of this paper is to calculate the composition of the assembly map with the Chern character in entire cyclic homology . We prove an index theorem reducing this computation to a cup-product in bivariant entire cyclic cohomology. As a consequence we obtain an explicit localization formula which includes, as particular cases, the equivariant Atiyah-Segal-Singer index theorem when G is compact, and the Connes-Moscovici index theorem for G-coverings when G is discrete. The proof is based on the bivariant Chern character introduced in previous papers.

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 The transverse index theorem for proper cocompact actions of Lie groupoids

2015 ◽  
Vol 99 (3) ◽  
pp. 443-472 ◽  
Author(s):  
Markus J. Pflaum ◽  
Hessel Posthuma ◽  
Xiang Tang
Keyword(s):  
Index Theorem ◽  
Lie Groupoids ◽  
Transverse Index
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