23 research outputs found
Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras with infinite dimensional coefficients
We discuss a new strategy for the computation of the Hopf-cyclic cohomology
of the Connes-Moscovici Hopf algebra . More precisely, we
introduce a multiplicative structure on the Hopf-cyclic complex of
, and we show that the van Est type characteristic homomorphism
from the Hopf-cyclic complex of to the Gelfand-Fuks cohomology
of the Lie algebra of formal vector fields on respects
this multiplicative structure. We then illustrate the machinery for .Comment: Minor revisions to highlight the main result
Hopf-cyclic homology and cohomology with coefficients
Following the idea of an invariant differential complex, we construct
general-type cyclic modules that provide the common denominator of known cyclic
theories. The cyclicity of these modules is governed by Hopf-algebraic
structures. We prove that the existence of a cyclic operator forces a
modification of the Yetter-Drinfeld compatibility condition leading to the
concept of a stable anti-Yetter-Drinfeld module. This module plays the role of
the space of coefficients in the thus obtained cyclic cohomology of module
algebras and coalgebras, and the cyclic homology and cohomology of comodule
algebras. Along the lines of Connes and Moscovici, we show that there is a
pairing between the cyclic cohomology of a module coalgebra acting on a module
algebra and closed 0-cocycles on the latter. The pairing takes values in the
usual cyclic cohomology of the algebra. Similarly, we argue that there is an
analogous pairing between closed 0-cocycles of a module coalgebra and the
cyclic cohomology of a module algebra