- Full text PDF available (15)
We classify extensions of certain classifiable C *-algebras using the six term exact sequence in K-theory together with the positive cone of the K 0-groups of the distinguished ideal and quotient. We then apply our results to a class of C *-algebras arising from substitutional shift spaces.
These notes are based on the six-hour Appalachian Set Theory workshop given by Ilijas Farah on February 9th, 2008 at Carnegie Mellon University. The first half of the workshop (Sections 1-3) consisted of a review of Hilbert space theory and an introduction to C *-algebras, and the second half (Sections 4–6) outlined a few set-theoretic problems relating to… (More)
In this paper we extend the classification results obtained by Rørdam in the paper . We prove a strong classification theorem for the unital essential extensions of Kirchberg algebras, a classification theorem for the non-stable, non-unital essential extensions of Kirchberg algebras, and we characterize the range in both cases. The invariants are cyclic… (More)
At the cost of restricting the nature of the involved K-groups, we prove a classification result for a hitherto unexplored class of graph C *-algebras, allowing us to classify all graph C *-algebras on finitely many vertices with a finite linear ideal lattice if all pair of vertices are connected by infinitely many edges when they are connected at all.
Semigroup C*-algebras for right-angled Artin monoids were introduced and studied by Crisp and Laca. In the paper at hand, we are able to present the complete answer to their question of when such C*-algebras are isomorphic. The answer to this question is presented both in terms of properties of the graph defining the Artin monoids as well as in terms of… (More)
We establish axiomatic characterizations of K-theory and KK-theory for real C*-algebras. In particular, let F be an abelian group-valued functor on separable real C*-algebras. We prove that if F is homotopy invariant, stable, and split exact, then F factors through the category KK. Also, if F is homotopy invariant , stable, half exact, continuous, and… (More)
We classify real Kirchberg algebras using united K-theory. Precisely, let A and B be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that A C and B C are also simple. In the stable case, A and B are iso-morphic if and only if K CRT (A) ∼ = K CRT (B). In the unital case, A and B are isomorphic if… (More)
We give a classification theorem for a class of C*-algebras which are direct limits of finite direct sums of E 0-algebras. The invariant consists of the following: (1) the set of Murray-von Neumann equivalence classes of projections; (2) the set of homotopy classes of hyponormal partial isometries; (3) a map d; and (4) total K-theory.
In 2006, Restorff completed the classification of all Cuntz-Krieger algebras with finitely many ideals (i.e., those that are purely infinite) up to stable isomorphism. He left open the questions concerning strong classification up to stable isomorphism and unital classification. In this paper, we address both questions. We show that any isomorphism between… (More)
The original version of this note was based on two talks given by Efren Ruiz at the Toronto Set Theory seminar in November 2005. This very tentative note and my Luminy talk form an attempt to record the ideas from these talks and draw more attention of set theorists to Naimark's problem (Problem 5.1 below). An excellent invitation to C*-algebras for… (More)