On the classification problem for C*-algebras

الأصل · EN

In the given article it is introduced new notions of a C*-algebra of von Neumann type I and C*-algebras of types Iₙ, II, II₁, II∞ and III. It is proved that any GCR-algebra is a C*-algebra of von Neumann type I, and a C*-algebra is an NGCR-algebra if and only if this C*-algebra does not have a nonzero Abelian annihilator. Also an analog of the theorem on decomposition of a von Neumann algebra to subalgebras of types I, II and III is proved. In the final part it is proved that every C*-factor of von Neumann type I is a C*-algebra of type Iₙ for some cardinal number n, every simple C*-algebra of type II₁ is finite, every simple purely infinite C*-algebra is of type III and every W*-factor of type II∞ has a simple C*-subalgebra of type II∞. Finally it is formulated a classification theorem for C*-factors.