2004/12/22 by Nikolai Neumaier, Neumaier, Nikolai, Markus J. Pflaum +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.KT #math.MP #math.SG
paper · pdf · doi:10.48550/arxiv.math/0412462
A few minor corrections have been made in the preliminaries, and Section 6.3 has been improved. The article will appear in Journal fuer die Reine und Angewandte Mathematik
openalex publication_date 2004/12/22 · arxiv created 2005/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper etale Lie groupoid is studied. We compute the Hochschild cohomology of the convolution algebra and express it in terms of alternating multi-vector fields on the associated inertia groupoid. We introduce a noncommutative Poisson homology whose computation enables us to determine the Hochschild homology of formal deformations of the convolution algebra. Then it is shown that the cyclic (co)homology of such formal deformations can be described by an appropriate sheaf cohomology theory. This enables us to determine the corresponding cyclic homology groups in terms of orbifold cohomology of the underlying orbifold. Using the thus obtained description of cyclic cohomology of the deformed convolution algebra, we give a complete classification of all traces on this formal deformation, and provide an explicit construction.