The Elliott Programme seeks classification of simple, separable, nuclear C∗-algebras via a functor based on K-theory. There are a handful of C∗-algebras, including the Cuntz algebras O2 and O∞, that play particularly important roles in the programme. It is principally in this context that the Jiang-Su algebra Z is regarded as an analogue of O∞, and this thesis proposes an analogue of O2 in a si...

Various subsets of the tracial state space of a unital C∗-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II1-factor representations of a class of C ∗-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II1-factor representations. This general theory is related to various ot...

Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

1. Topologies on B(H) and the double commutant theorem 2 2. Examples of von Neumann algebras 5 2.1. Abelian von Neumann algebras 6 2.2. Group von Neumann algebras and representation theory 6 2.3. The Hyperfinite II1 factor R 9 3. Projections, Type Classification, and Traces 10 3.1. Projections and the spectral theorem 10 3.2. Type classification of factors 12 3.3. Traces 13 4. Tracial ultrapowe...

in this work, using eigenvalues and eigenvectors of unitary cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing pst occurring in its unitary cayley graph. moreover, we have some developments when $r$ is a product of local rings.

Let C and A be two unital separable amenable simple C-algebras with tracial rank no more than one. Suppose that C satisfies the Universal Coefficient Theorem and suppose that φ1, φ2 : C → A are two unital monomorphisms. We show that there is a continuous path of unitaries {ut : t ∈ [0,∞)} of A such that lim t→∞ u∗tφ1(c)ut = φ2(c) for all c ∈ C if and only if [φ1] = [φ2] in KK(C,A), φ ‡ 1 = φ 2 ...

In [Oz], Ozawa obtained analogues of the Kurosh subgroup theorem (and its consequences) in the setting of free products of semiexact II1 factors with respect to the canonical tracial states. In particular he was able to prove a certain unique-factorization theorem that distinquishes, for example, the n-various L(F∞) ∗ (L(F∞)⊗ R) . The paper was a continuation of the joint work [OP] with Popa th...