Quantum sections and Gauge algebras

Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring . The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring ; these are the socalled gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories . The paper surveys basic definitions and properties but concentrates on the development of several concrete examples

Noncommutative geometry of angular momentum space U(su(2))

We study the standard angular momentum algebra $[x_i,x_j]=i\lambda \epsilon_{ijk}x_k$ as a noncommutative manifold $R^3_\lambda$. We show that there is a natural 4D differential calculus and obtain its cohomology and Hodge * operator. We solve the spin 0 wave equation and some aspects of the Maxwell or electromagnetic theory including solutions for a uniform electric current density, and we find a natural Dirac operator. We embed $R^3_\lambda$ inside a 4D noncommutative spacetime which is the limit $q\to 1$ of q-Minkowski space and show that $R^3_\lambda$ has a natural quantum isometry group given by the quantum double $D(U(su(2)))$ as a singular limit of the $q$-Lorentz group. We view $\R^3_\lambda$ as a collection of all fuzzy spheres taken together. We also analyse the semiclassical limit via minimum uncertainty states $|j,\theta,\phi>$ approximating classical positions in polar coordinates.Comment: Minor revision to add reference [11]. 37 pages late

An Imaging and Spectroscopic Study of the z=3.38639 Damped Lyman Alpha System in Q0201+1120: Clues to Star Formation Rate at High Redshift

We present the results of a series of imaging and spectroscopic observations aimed at identifying and studying the galaxy responsible for the z = 3.38639 damped lya system in the z = 3.61 QSO Q0201+1120. We find that the DLA is part of a concentration of matter which includes at least four galaxies (probably many more) over linear comoving dimensions, greater than 5h^-1Mpc. The absorber may be a 0.7 L* galaxy at an impact parameter of 15 h^-1 kpc, but follow-up spectroscopy is still required for positive identification. The gas is turbulent, with many absorption components distributed over approximately 270 km/s and a large spin temperature, T_s greater than 4000K. The metallicity is relatively high for this redshift, Z(DLA) approximately 1/20 Z(solar). From consideration of the relative ratios of elements which have different nucleosynthetic timescales, it would appear that the last major episode of star formation in this DLA occurred at z greater than 4.3, more than approximately 500 Myr prior to the time when we observe it.Comment: Accepted for publication in Ap

The Ideal Intersection Property for Groupoid Graded Rings

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property

Middle Convolution and Harnad Duality

We interpret the additive middle convolution operation in terms of the Harnad duality, and as an application, generalize the operation to have a multi-parameter and act on irregular singular systems.Comment: 50 pages; v2: Submitted version once revised according to referees' comment

On quiver Grassmannians and orbit closures for representation-finite algebras

We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation- nite algebra, we use the projective quotient algebra to construct desingularizations of quiver Grassmannians, orbit closures in representation varieties, and their desingularizations. This generalizes results of Cerulli Irelli, Feigin and Reineke

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Eosinophils are part of the granulocyte response in tuberculosis and promote host resistance in mice

Host resistance to Mycobacterium tuberculosis (Mtb) infection requires the activities of multiple leukocyte subsets, yet the roles of the different innate effector cells during tuberculosis are incompletely understood. Here we uncover an unexpected association between eosinophils and Mtb infection. In humans, eosinophils are decreased in the blood but enriched in resected human tuberculosis lung lesions and autopsy granulomas. An influx of eosinophils is also evident in infected zebrafish, mice, and nonhuman primate granulomas, where they are functionally activated and degranulate. Importantly, using complementary genetic models of eosinophil deficiency, we demonstrate that in mice, eosinophils are required for optimal pulmonary bacterial control and host survival after Mtb infection. Collectively, our findings uncover an unexpected recruitment of eosinophils to the infected lung tissue and a protective role for these cells in the control of Mtb infection in mice

Measurement of the Bs0→J/ψKS0B_s^0\to J/\psi K_S^0 branching fraction

The $B_s^0\to J/\psi K_S^0$ branching fraction is measured in a data sample corresponding to 0.41$fb^{-1}$ of integrated luminosity collected with the LHCb detector at the LHC. This channel is sensitive to the penguin contributions affecting the sin2$\beta$ measurement from $B^0\to J/\psi K_S^0$ The time-integrated branching fraction is measured to be $BF(B_s^0\to J/\psi K_S^0)=(1.83\pm0.28)\times10^{-5}$. This is the most precise measurement to date

Measurement of the mass and lifetime of the Ωb−\Omega_b^- baryon

A proton-proton collision data sample, corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by LHCb at $\sqrt{s}=7$ and 8 TeV, is used to reconstruct $63\pm9$ $\Omega_b^-\to\Omega_c^0\pi^-$, $\Omega_c^0\to pK^-K^-\pi^+$ decays. Using the $\Xi_b^-\to\Xi_c^0\pi^-$, $\Xi_c^0\to pK^-K^-\pi^+$ decay mode for calibration, the lifetime ratio and absolute lifetime of the $\Omega_b^-$ baryon are measured to be \begin{align*} \frac{\tau_{\Omega_b^-}}{\tau_{\Xi_b^-}} &= 1.11\pm0.16\pm0.03, \\ \tau_{\Omega_b^-} &= 1.78\pm0.26\pm0.05\pm0.06~{\rm ps}, \end{align*} where the uncertainties are statistical, systematic and from the calibration mode (for $\tau_{\Omega_b^-}$ only). A measurement is also made of the mass difference, $m_{\Omega_b^-}-m_{\Xi_b^-}$, and the corresponding $\Omega_b^-$ mass, which yields \begin{align*} m_{\Omega_b^-}-m_{\Xi_b^-} &= 247.4\pm3.2\pm0.5~{\rm MeV}/c^2, \\ m_{\Omega_b^-} &= 6045.1\pm3.2\pm 0.5\pm0.6~{\rm MeV}/c^2. \end{align*} These results are consistent with previous measurements.Comment: 11 pages, 5 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-008.htm