George A. Elliott

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A category is described to which the Cuntz semigroup belongs and as a functor into which it preserves inductive limits. 1. Recently, Toms in [26] used the refinement of the invariant K0 introduced by Cuntz almost thirty years ago in [4] to show that certain C*-algebras are not isomorphic. Anticipating the possible use of this invariant to establish(More)
We report on recent progress in the program to classify separable amenable C∗-algebras. Our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank, strict comparison of positive elements, and Z-stability, and on the importance of the Cuntz semigroup. We include a brief history of the program’s successes since 1989,(More)
A common generalization is given of what are often referred to as the Weyl–von Neumann theorems of Voiculescu, Kasparov, Kirchberg, and, more recently, Lin. (These in turn extend a result of Brown, Douglas, and Fillmore.) More precisely, an intrinsic characterization is obtained of those extensions of one separable C∗-algebra by another—the first, i.e., the(More)
It is shown that, for a C*-algebra of stable rank one (i.e., in which the invertible elements are dense), two well-known isomorphism invariants, the Cuntz semigroup and the Thomsen semigroup, contain the same information. More precisely, these two invariants, viewed appropriately, determine each other in a natural way. 1. In [4], Cuntz introduced an(More)
We prove that all unital separable continuous fields of C*-algebras over [0, 1] with fibers isomorphic to the Cuntz algebra On (2 ≤ n ≤ ∞) are trivial. More generally, we show that if A is a separable, unital or stable, continuous field over [0, 1] of Kirchberg C*-algebras satisfying the UCT and having finitely generated K-theory groups, then A is(More)
A heat-stable protein has recently been isolated from the submaxillary gland of the male mouse which, upon injection, elicits precocious eyelid separation and tooth eruption in the newborn mouse and rat (1). The eyelids of the treated newborn mouse will separate as early as the sixth day after birth, whereas the eyelids of control animals require twelve to(More)
Considerable attention has recently focused on the role of inflammation in the pathophysiology of asthma, with special emphasis on "late-phase" bronchoconstriction and increased airway hyperreactivity after antigen challenge in sensitized subjects. The present report describes the histopathologic changes in guinea-pig lung and trachea at various time(More)
Diphosphonates (DP) are synthetic pyrophosphates with a P-C-P backbone and are predominantly used for the treatment of bone diseases. Several DP have also been shown to exert significant antiarthritic effects in the rat adjuvant-induced polyarthritis model; however, there is no direct evidence for the anti-inflammatory effects of these compounds. We(More)