C*-algebras associated with higher-dimensional noncommutative simplicial complexes and their K-theory

Universal C*-Algebras associated with noncommutative simplicial complexes were introduced recentely by J.Cuntz. The K-theory of these C*-algebras give an explanation for the Baum-Connes conjecture. Our main aim is to determines the K-theory of such algebras. By using the skeleton filtrations of thes...

Author: Omran, Saleh
Further contributors: Cuntz, Joachim (Thesis advisor)
Division/Institute:FB 10: Mathematik und Informatik
Document types:Doctoral thesis
Media types:Text
Publication date:2005
Date of publication on miami:01.09.2005
Modification date:18.02.2016
Edition statement:[Electronic ed.]
Subjects:K-theory; Noncommutative simplical complexes; Universal C*-algebras; Baum-Connes conjecture
DDC Subject:510: Mathematik
License:InC 1.0
Language:English
Format:PDF document
URN:urn:nbn:de:hbz:6-35619656065
Permalink:http://nbn-resolving.de/urn:nbn:de:hbz:6-35619656065
Digital documents:diss_omran
01_diss_omran.pdf
02_diss_omran.pdf
DownloadFiles:ZIP File

Universal C*-Algebras associated with noncommutative simplicial complexes were introduced recentely by J.Cuntz. The K-theory of these C*-algebras give an explanation for the Baum-Connes conjecture. Our main aim is to determines the K-theory of such algebras. By using the skeleton filtrations of these algebras we can analyze the topological information of these algebras. The K-theory of the universal C*-algebras associated with noncommutative simplical complexes and the K-theory of the algebras of continous functions on the geometric realization of the simplicial complexes are not identical in general. We obtained in ditales such situations when the algebras above are identical in K-theory. We introduced a Unversal C*-algebras associated with certain simplical complexes and computed Its K-theory.