We define and study equivariant periodic cyclic homology for locally compact groups. This can be viewed as a noncommutative generalization of equivariant de Rham cohomology. Although the construction resembles the Cuntz-Quillen approach to ordinary cyclic homology, a completely new feature in the equivariant setting is the fact that the basic ingredient in the theory is not a complex in the usu...

ABSTRACT This paper reports a new method for measurement of periodic flows with phase-sampling technique by using conventional micro particle image velocimetry (PIV). Non-integer multiples for the laser pulse frequency and the frequency of the periodic flow are chosen such that each velocimetry data set represents a unique point in phase for the periodic flow. The method we proposed does not re...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

We generalise the known excision results for Hochschild, cyclic and periodic cyclic homology to algebras in symmetric monoidal categories. Our abstract result also contains excision for extensions of nuclear H-unital Fréchet algebras. As an application, we compute the Hochschild and cyclic homology of the algebra of Whitney functions on an arbitrary closed subset of a smooth manifold, and the p...