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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 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.