C*-algebras associated to Boolean dynamical systems

The goal of this talk is to present the C*-algebra $C^*(\mathcal{B}, \mathcal{L}, \theta)$ of a Boolean dynamical system $(\mathcal{B}, \mathcal{L}, \theta)$, that generalizes the $C^*$-algebra associated to a labelled graph introduced by Bates and Pask, and to determine its simplicity, its gauge invariant ideals, as well as compute its K-Theory. This is a joint work with Toke Meier Carlsen (Department of Science and Technology, University of the Faroe Islands) and Eduard Ortega (Department of Mathematical Sciences, NTNU Trondheim).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Purely infinite crossed products by endomorphisms

We study the crossed product $C^*$-algebra associated to injective endomorphisms, which turns out to be equivalent to study the crossed product by the dilated autormorphism. We prove that the dilation of the Bernoulli $p$-shift endomorphism is topologically free. As a consequence, we have a way to twist any endomorphism of a \D-absorbing $C^*$-algebra into one whose dilated automorphism is essentially free and have the same $K$-theory map than the original one. This allows us to construct purely infinite crossed products $C^*$-algebras with diverse ideal structures.Comment: Corrected misprints. Clarified some points in Section 3. Added a reference. Re-submitted to JMA

Formas de ocupación rural en la sierra norte de Guadalajara (siglos V-X): el despoblado de Morenglos (Alcolea de las Peñas, Guadalajara)

La presente comunicación pretende acercarse al tránsito de la antigüedad a la edad media en la sierra norte de Guadalajara (España) en lo que el poblamiento rural y el territorio se refiere. Debido a la ausencia de estudios previos sobre este territorio, hemos realizado un vaciado documental exhaustivo de cara a establecer un panorama previo para el análisis del poblamiento rural de la zona entre los siglos V y X. En este sentido, hemos llevado a cabo un trabajo de campo, del que presentamos algunos resultados, concretamente en torno al despoblado y espacios rupestres de Morenglos (Alcolea de las Peñas, Guadalajara), bien se trate de estructuras de habitación o de necrópolis, y que nos servirán como ejemplo para acercamos a un elenco mucho más amplio de hábitat rupestres en toda la Sierra Norte de Guadalajara que se extiende hasta el sur de la provincia de Soria.L'object de cette comunication est d'arriver à une approximation de la transition de I'Antiquité au Moyen Áge, dans le territoire de la Chaîne Nort de Guadalajara (Espagne), en ce qui concerne le peuplement rural et I'occupation du territoire. Etant donnée I'absence d'études de base pour ce territoire, nous avons réalisé une étude documentale intensive a fin d'établir le panorama préalable pour I'analyse du peuplement rural de la zone, pendant les siècles V à X. Dans ce but, nous réalisé des travaux de champs, dont nous présentons certains des résultats, en particulier aux allentours du dépueplé de Morenglos (Alcolea de la Peñas, Guadalajara), étant celui-ci un ensemble de structures habitationelles, ou nécropole, qui nous servirá comme exemple pour nous approcher a une réalité bien plus importante d'habitat rupestre dans le cadre de la Chaîne Nort de Guadalajara qui s'étend jusqu'à la region de Soria

San Salvador de Pinilla durante el s. XIII (1218-1300). Aportaciones para su estudio

Estudio histórico documental de la documentación relativa al siglo XIII sobre el edificio medieval y de la comunidad monástica que lo habitó (1218-1575

Finite projections in multiplier algebras

We give a characterization of finiteness of projections in the multiplier algebra of a σ-unital C∗-algebra of realran k zero and stable rank one

Metric completions of ordered groups and K0+of exchange rings

We give a description of the closure of the natural a ne contin- uous function representation of K0(R) for any exchange ring R. This goal is achieved by extending the results of Goodearl and Handelman, about metric completions of dimension groups, to a more general class of pre-ordered groups, which includes K0 of exchange rings. As a consequence, the results about K+ 0 of regular rings, which the author gave in an earlier paper, can be extended to a wider class of rings, which includes C -algebras of real rank zero, among others. Also, the framework of pre-ordered groups developed here allows other potential applications

Dilations and full corners on fractional skew monoid rings

In this note we will show that the dilation result obtained for fractional skew monoid rings, in the case of a cancellative left Ore monoid S acting on a unital ring A by corner isomorphisms, holds in full generality. We apply this result to the context of semigroup C -crossed products

On a density condition for K0+ of von Neumann regular rings

P.Ara and K.R.Goodearl, in [1], introduced and studied the concept of a regular ring R satisfying the following condition, which they called condition is dense in Aff(S(Ko(R)[R]))†, where Φ denotes the natural map from Ko(R) to Aff(S(Ko(R)[R])). They proved that every nonartinian, stably finite, strictly unperforated, simple regular ring satisfies condition (D). In this note we prove that a regular ring R satisfies condition (D) if and only if R has no nonzero artinian homomorphic image. We then obtain as a consequence that every nonartinian, simple regular ring satisfies condition (