Necessary conditions for various algebraic types of the Weyl tensor are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically special, of type Ii, while locally on the horizon the type is II. One exceptional subclass – the Myers-Perry solution – is of type D.

Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to wN -Atkin-Lehner twists of most modular curves X0(N) and to wp-Atkin-Lehner twists of certain Shimura curves XD+.

We characterize cosieves in locally presentable categories which are generated by a set of objects or are even principal. We apply our results to the category of algebraic theories where they are related to Mal’cev conditions dealt with in universal algebra.

In this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four-manifold can be arbitrarily large. The examples that we consider in this paper are locally simple abelian covers of rational surfaces. The proof involves the algebraic description of rational blow down, classical Brill-Noether theory and deformation theory of normal flat abelian covers.

An algebra A is called a GI-algebra if its group of units A satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite? 2000Mathematics Subject Classification. 16R40; 16R50; 16U60; 17B35.

We point some contributions to the construction of Locally Recoverable codes from algebraic curves recently presented by A. Barg, I. Tamo and S. Vladut, that can lead to improvements concerning the definition, the parameters and the local recovering of these codes.

We introduce C∗-pseudo-multiplicative unitaries and (concrete) Hopf C∗-bimodules, which are C∗-algebraic variants of the pseudo-multiplicative unitaries on Hilbert spaces and the Hopf-von Neumann-bimodules studied by Enock, Lesieur, and Vallin [5, 6, 4, 10, 19, 20]. Moreover, we associate to every regular C∗-pseudo-multiplicative unitary two Hopf-C∗bimodules and discuss examples related to loca...

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

Osserman manifolds are a generalization of locally two-point homogeneous spaces. We introduce k-root in which the reduced Jacobi operator has exactly k eigenvalues. investigate one-root and two-root as another prove that there is no Riemannian manifold odd dimension. In twice an dimension, we describe all algebraic curvature tensors give additional conditions for manifolds.

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals