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In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-abelian group G for which every non-linear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary abelian 2-group.
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)
We give a classification theorem for a class of C*-algebras which are direct limits of finite direct sums of E0-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.
We classify real Kirchberg algebras using united Ktheory. Precisely, let A and B be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that AC and BC are also simple. In the stable case, A and B are isomorphic if and only if K(A) ∼= K(B). In the unital case, A and B are isomorphic if and only if (K… (More)
We show that the absence of equilibrium states of two uncharged spinning particles located on the symmetry axis, revealed in an approximate approach recently employed by Bonnor, can be explained by a non–general character of his approximation scheme which lacks an important arbitrary parameter representing a strut. The absence of this parameter introduces… (More)
We initiate the study of absorbing representations of C-algebras with respect to closed operator convex cones. We completely determine when such absorbing representations exist, which leads to the question of characterising when a representation is absorbing, as in the classical Weyl–von Neumann type theorem of Voiculescu. In the classical case, this was… (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)
For a certain class of extensions e : 0 → B → E → A → 0 of C∗-algebras in which B and A belong to classifiable classes of C∗-algebras, we show that the functor which sends e to its associated six term exact sequence in K-theory and the positive cones of K0(B) and K0(A) is a classification functor. We give two independent applications addressing the… (More)