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- EFREN RUIZ
- 2006

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.

- ILIJAS FARAH, ERIC WOFSEY, +4 authors Nik Weaver
- 2008

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)

- GUNNAR RESTORFF, EFREN RUIZ
- 2006

In this paper we extend the classification results obtained by Rørdam in the paper [15]. 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)

- Søren Eilers, E. Ruiz
- 2010

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.

It is said that the vorticity of a congruence plays the role of rate of rotation for the precession of a gyroscope moving along a world-line belonging to the congruence. Our aim is to determine the evolution equation for the angular momentum of a gyrosocope with respect to an arbitrary time-like congruence, i.e, a reference congruence which does not contain… (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 show that the well–known NUT solution can be correctly interpreted as describing the exterior field of two counter–rotating semi– infinite sources possessing negative masses and infinite angular mo-menta which are attached to the poles of a static finite rod of positive mass.

- Jeffrey L. Boersema, Efren Ruiz, P. J. Stacey, Joachim Cuntz
- 2011

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)

The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate… (More)

- EFREN RUIZ
- 2005

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.