1,985 research outputs found
The periodic cyclic homology of crossed products of finite type algebras
We study the periodic cyclic homology groups of the cross-product of a finite
type algebra by a discrete group . In case is commutative and
is finite, our results are complete and given in terms of the singular
cohomology of the strata of fixed points. These groups identify our cyclic
homology groups with the \dlp orbifold cohomology\drp\ of the underlying
(algebraic) orbifold. The proof is based on a careful study of localization at
fixed points and of the resulting Koszul complexes. We provide examples of
Azumaya algebras for which this identification is, however, no longer valid. As
an example, we discuss some affine Weyl groups.Comment: Funding information adde
On the Topological Interpretation of Gravitational Anomalies
We consider the mixed gravitational-Yang-Mills anomaly as the coupling
between the -theory and -homology of a -algebra crossed product. The
index theorem of Connes-Moscovici allows to compute the Chern character of the
-cycle by local formulae involving connections and curvatures. It gives a
topological interpretation to the anomaly, in the sense of noncommutative
algebras.Comment: 16 pages, LaTex, no figure
A Riemann-Roch Theorem For One-Dimensional Complex Groupoids
We consider a smooth groupoid of the form \Sigma\rtimes\Gamma where \Sigma is
a Riemann surface and \Gamma a discrete pseudogroup acting on \Sigma by local
conformal diffeomorphisms. After defining a K-cycle on the crossed product
C_0(\Sigma)\rtimes\Gamma generalising the classical Dolbeault complex, we
compute its Chern character in cyclic cohomology, using the index theorem of
Connes and Moscovici. This involves in particular a generalisation of the Euler
class constructed from the modular automorphism group of the von Neumann
algebra L^{\infty}(\Sigma)\rtimes\Gamma.Comment: 20 pages, LaTex, minor change
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