NETS OF GRADED C*-ALGEBRAS OVER PARTIALLY ORDERED SETS

摘要

The paper deals with C*-algebras generated by a net of Hilbert spaces over a partially ordered set. The family of those algebras constitutes a net of C*-algebras over the same set. It is shown that every such algebra is graded by the first homotopy group of the partially ordered set. Inductive systems of C*-algebras and their limits over maximal directed subsets are considered, as well as properties of morphisms for nets of Hilbert spaces and nets of C*-algebras.