Cyclic Cohomology and Hopf Algebra Symmetry

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Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category (2005, methodology): “Namely, for α = β = idH , we obtain the usual Yetter-Drinfeld modules; for α = S 2, β = idH , we obtain the so-called anti-Yetter-Drinfeld modules, introduced in [7], [8], [10] as coefficients for the cyclic cohomology of Hopf algebras defined by Connes and Moscovici in [5], [6]; finally, an (idH , ”
A New Cyclic Module for Hopf Algebras (2000, methodology): “For k = R, this gives an alternative proof of Proposition 4 and Remark 5 in [ 3 ].”
Differentiable cyclic cohomology and Hopf algebraic structures in transverse geometry (2001, methodology): “Application to the transverse index formula We shall now indicate how the preceding results apply to the cohomological index formula for the transverse fundamental class in K-homology (cf. [9], [10], [12]), in the setting of diﬀeomorphism invariant geometry. With the manifold M assumed to be oriente”
Lectures on Noncommutative Geometry (2005, background): “(Connes-Moscovici Hopf algebras) A very important example for noncommutative geometry and its applications to transverse geometry and number theory is the family of Connes-Moscovici Hopf algebras Hn for n ≥ 0 [39, 40, 41].”