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A Classification Theorem for Nuclear Purely Infinite Simple C -Algebras 1
Starting from Kirchberg's theorems announced at the operator algebra conference in Gen eve in 1994, namely O2 A = O2 for separable unital nuclear simple A and O1 A = A for separable unital nuclearExpand
Crossed Products of the Cantor Set by Free Minimal Actions of ℤd
Let d be a positive integer, let X be the Cantor set, and let ℤd act freely and minimally on X. We prove that the crossed product C*(ℤd,X) has stable rank one, real rank zero, and cancellation ofExpand
The tracial Rokhlin property for actions of finite groups on C*-algebras
We define ``tracial'' analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and approximate innerness. We prove the followingExpand
Recursive subhomogeneous algebras
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursiveExpand
We define K-theory for Frechet algebras (assumed to be locally multiplicatively convex) so as to simultaneously generalize K-theory for σ-C*-algebras and K-theory for Banach algebras. The mainExpand
The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
Abstract Let F ⊆ SL2(ℤ) be a finite subgroup (necessarily isomorphic to one of ℤ2, ℤ3, ℤ4, or ℤ6), and let F act on the irrational rotational algebra Aθ via the restriction of the canonical action ofExpand
Crossed products by finite cyclic group actions with the tracial Rokhlin property
We define the tracial Rokhlin property for actions of finite cyclic groups on stably finite simple unital C*-algebras. We prove that when the algebra is in addition simple and has tracial rank zero,Expand
Analogs of Cuntz algebras on Lp spaces
For $d = 2, 3, \ldots$ and $p \in [1, \infty),$ we define a class of representations $\rho$ of the Leavitt algebra $L_d$ on spaces of the form $L^p (X, \mu),$ which we call the spatialExpand