On algebraic homogeneous spaces

On the Geometry of Algebraic Groups and Homogeneous Spaces

Given a connected algebraic group G over an algebraically closed field and a G-homogeneous space X , we describe the Chow ring of G and the rational Chow ring of X , with special attention to the Picard group. Also, we investigate the Albanese and the “anti-affine” fibrations of G and X .

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

Algebraic Homogeneous Spaces over Fields of Characteristic Two

Flows on Homogeneous Spaces

We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain ows on homogeneous spaces. This approach yields a new proof of a conjecture of Mahler, originally settled by V. G. Sprind zuk in 1964. We also prove several related hypotheses of Baker and Sprind zuk formulated in 1970...

Algebraic distance in algebraic cone metric spaces and its properties

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.