Solleveld Maarten Sander (1 results)

[S.l. : s.n.], 2007. Paperback. 253 pp. Proefschrift Universiteit van Amsterdam. - This dissertation investigates periodic cyclic homology in the setting of affine Hecke algebras and their connections with K-theory, representation theory, and noncommutative geometry. It begins with an introduction to algebraic, topological, and periodic cyclic homology, together with their relations to topological K-theory through the Chern character and to equivariant cohomology. The core of the thesis is devoted to affine Hecke algebras. After presenting their definitions and representation theory, the Fourier transform is developed and used to analyze their periodic cyclic homology. The work then extends these methods to Hecke algebras arising from reductive p-adic groups, including Harish-Chandra's Schwartz algebra, the Plancherel theorem, and noncommutative geometric aspects. A major part of the thesis studies how periodic cyclic homology behaves under parameter deformations of affine Hecke algebras, with special attention to equal label and finite-dimensional cases, norm estimates, and scaling of parameters. These deformations are related to K-theoretic conjectures. The final chapter provides explicit examples and calculations illustrating the general theory. Condition : copy. ISBN 9789090215433. Keywords : MATHEMATICS,