On the Hopf-type Cyclic Cohomology with Coefficients

2006 ◽  
pp. 203-212 ◽  
Author(s):  
I. M. Nikonov ◽  
G. I. Sharygin
Keyword(s):  
Cyclic Cohomology

scholarly journals Higher spectral flow and an entire bivariant JLO cocycle

2012 ◽  
Vol 11 (1) ◽  
pp. 183-232 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
Alan L. Carey
Keyword(s):  
Dirac Operator ◽  
Chern Character ◽  
Dirac Operators ◽  
Cyclic Cohomology ◽  
Closed Manifold ◽  
Spectral Flow ◽  
Smooth Functions ◽  
Base Manifold ◽  
K Theory ◽  
Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

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 Algebraic connections, universal bimodules and entire cyclic cohomology

1994 ◽  
Vol 161 (3) ◽  
pp. 433-446 ◽  
Author(s):  
Masoud Khalkhali
Keyword(s):  
Cyclic Cohomology

scholarly journals Cyclic cohomology after the excision theorem of Cuntz and Quillen

2013 ◽  
Vol 11 (3) ◽  
pp. 575-598
Author(s):  
Jacek Brodzki
Keyword(s):  
Exact Sequence ◽  
Cyclic Cohomology ◽  
New Formalism ◽  
Remarkable Result ◽  
The Creation

AbstractThe excision theorem of Cuntz and Quillen established the existence of a six term exact sequence in the bivariant periodic cyclic cohomology HP*(–,–) associated with an arbitrary algebra extension 0 → S → P → Q → 0. This remarkable result enabled far reaching developments in the purely algebraic periodic cyclic cohomology. It also provided a new formalism that led to the creation of new versions of this theory for topological and bornological algebras. In this article we outline some of the developments that resulted from this breakthrough.

Cyclic cohomology of (extended) Hopf algebras

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

A Note on the Entire Cyclic Cohomology of a Finite Dimensional Noncommutative Space

1993 ◽  
Vol 36 (4) ◽  
pp. 449-457
Author(s):  
Slawomir Klimek ◽  
Andrzej Lesniewski
Keyword(s):  
Sufficient Conditions ◽  
Cyclic Cohomology ◽  
Noncommutative Space ◽  
Finite Dimensional ◽  
Noncommutative Spaces

AbstractWe present sufficient conditions for entire cyclic cohomology to reduce to ordinary cyclic cohomology. These conditions are characteristic for finite dimensional (noncommutative) spaces.

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