Bounded and unitary elements in pro-C^*-algebras

A pro-C^*-algebra is a (projective) limit of C^*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C^*-algebras can be seen as non-commutative k-spaces. An element of a pro-C^*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C^*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C^*-algebra. In this paper, we investigate pro-C^*-algebras from a categorical point of view. We study the functor (-)_b that assigns to a pro-C^*-algebra the C^*-algebra of its bounded elements, which is the dual of the Stone-\v{C}ech-compactification. We show that (-)_b is a coreflector, and it preserves exact sequences. A generalization of the Gelfand-duality for commutative unital pro-C^*-algebras is also presented.Comment: v2 (accepted

Twisted equivariant K-theory, groupoids and proper actions

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.Comment: 26 page

Cartan subalgebras in C*-algebras of Hausdorff etale groupoids

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if and only if the interior of the isotropy in $G$ is closed. Using this, we prove that when the interior of the isotropy is abelian and closed, $M$ is a Cartan subalgebra. We prove that for a large class of groupoids $G$ with abelian isotropy---including all Deaconu--Renault groupoids associated to discrete abelian groups---$M$ is a maximal abelian subalgebra. In the specific case of $k$-graph groupoids, we deduce that $M$ is always maximal abelian, but show by example that it is not always Cartan.Comment: 14 pages. v2: Theorem 3.1 in v1 incorrect (thanks to A. Kumjain for pointing out the error); v2 shows there is a conditional expectation onto $M$ iff the interior of the isotropy is closed. v3: Material (including some theorem statements) rearranged and shortened. Lemma~3.5 of v2 removed. This version published in Integral Equations and Operator Theor

GPS observables in general relativity

I present a complete set of gauge invariant observables, in the context of general relativity coupled with a minimal amount of realistic matter (four particles). These observables have a straightforward and realistic physical interpretation. In fact, the technology to measure them is realized by the Global Positioning System: they are defined by the physical reference system determined by GPS readings. The components of the metric tensor in this physical reference system are gauge invariant quantities and, remarkably, their evolution equations are local.Comment: 6 pages, 1 figure, references adde

Twin Deficits or Distant Cousins? Evidence from India

The twin-deficits theory has intrigued economists and policy-makers alike for the past few decades. In a Keynesian economy, budget deficit increases the absorption of the economy, causes import expansions, and thereby, worsens the trade deficit. It also causes domestic interest rates to rise, domestic currency to appreciate, and thereby, contributes to trade deficits. However, according to the Ricardian Equivalence Hypothesis (REH), rising budget deficits implies higher future tax-liabilities so people would save more and consume less. As a result, an inter-temporal shift between taxes and budget deficits would have no impact on the real interest, or the trade deficit. Thus, the issue of whether the twin-deficits phenomenon holds becomes more of an empirical question, and the recent fiscal expansions to curb recession makes it timely to revisit the phenomenon, especially for the developing countries confronting both the deficits on a chronic basis. To this end, we make a case study of India, using the bounds-testing approach to cointegration and error-correction modeling on monthly and quarterly data over 1998-2009. Our results suggest that the twin-deficits theory holds for India in the short-run (validating the Keynesian channel) but not in the long run (validating the REH)

Risk Factors for Development of Chronic Kidney Disease in Cats

BACKGROUND: Identification of risk factors for development of chronic kidney disease (CKD) in cats may aid in its earlier detection. HYPOTHESIS/OBJECTIVES: Evaluation of clinical and questionnaire data will identify risk factors for development of azotemic CKD in cats. ANIMALS: One hundred and forty‐eight client‐owned geriatric (>9 years) cats. METHODS: Cats were recruited into the study and followed longitudinally for a variable time. Owners were asked to complete a questionnaire regarding their pet at enrollment. Additional data regarding dental disease were obtained when available by development of a dental categorization system. Variables were explored in univariable and multivariable Cox regression models. RESULTS: In the final multivariable Cox regression model, annual/frequent vaccination (P value, .003; hazard ratio, 5.68; 95% confidence interval, 1.83–17.64), moderate dental disease (P value, .008; hazard ratio, 13.83; 95% confidence interval, 2.01–94.99), and severe dental disease (P value, .001; hazard ratio, 35.35; 95% confidence interval, 4.31–289.73) predicted development of azotemic CKD. CONCLUSION: Our study suggests independent associations between both vaccination frequency and severity of dental disease and development of CKD. Further studies to explore the pathophysiological mechanism of renal injury for these risk factors are warranted

A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such an algebra has been moved to a separate paper (1309.4142 [math.OA]

Canonical Quantization of Spherically Symmetric Dust Collapse

Quantum gravity effects are likely to play a crucial role in determining the outcome of gravitational collapse during its final stages. In this contribution we will outline a canonical quantization of the LeMaitre-Tolman-Bondi models, which describe the collapse of spherical, inhomogeneous, non-rotating dust. Although there are many models of gravitational collapse, this particular class of models stands out for its simplicity and the fact that both black holes and naked singularity end states may be realized on the classical level, depending on the initial conditions. We will obtain the appropriate Wheeler-DeWitt equation and then solve it exactly, after regularization on a spatial lattice. The solutions describe Hawking radiation and provide an elegant microcanonical description of black hole entropy, but they raise other questions, most importantly concerning the nature of gravity's fundamental degrees of freedom.Comment: 19 pages no figures. Contribution to a festschrift in honor of Joshua N. Goldber

Categorizing Different Approaches to the Cosmological Constant Problem

We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future reference. We find that they all can be classified into five different schemes of which we indicate the advantages and drawbacks. Besides, we add a new approach based on a symmetry principle mapping real to imaginary spacetime.Comment: updated version, accepted for publicatio