Related papers: Orthogonal to principal ideles
We study graphs coming from quadratic spaces over finite fields via orthogonality which generalize a recent result given by Bishnoi, Ihringer, and Pepe (2019). More precisely, we study the graph $\Gamma^{\square}(n,k,q)$ as follows: the…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In…
By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and…
We establish a close and previously unknown relation between quantales and groupoids, in terms of which the notion of etale groupoid is subsumed in a natural way by that of quantale. In particular, to each etale groupoid, either localic or…
We describe and prove uniqueness of a natural homomorphism between some groups associated to finite sets.
The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…
We present those properties of planar doodles, especially when regarded as 4-valent graphs, that enable us to classify them into {\it prime} and {\it super prime} doodles by analogy to a knot sum. We describe a method for partially…
Associated to each material body $\mathcal{B}$ there exists a groupoid $\Omega \left( \mathcal{B} \right)$ consisting of all the material isomorphisms connecting the points of $\mathcal{B}$. The uniformity character of $\mathcal{B}$ is…
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite…
We give a one-to-one correspondence between ideals in the Steinberg algebra of a Hausdorff ample groupoid $G$, and certain families of ideals in the group algebras of isotropy groups in $G$. This generalises a known ideal correspondence…
The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these definitions are essentially equivalent.…
A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are…
This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.
We determine all the ideals of the homological Goldman Lie algebra, which reflects the structure of an oriented surface.
In this paper, we show how to apply a theorem by L\^e D.T. and the author about linear families of curves on normal surface singularities to get new results in this area. The main concept used is a specific definition of {\em general…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
This paper introduces the notion of prestacks of Tate type and studies natural geometric conditions on them. We also develop a formalism of Tate-coherent sheaves and define a dualizing gerbe for Tate schemes locally almost of finite type.
Given a smooth curve, the canonical representation of its automorphism group is the space of global holomorphic differential 1-forms as a representation of the automorphism group of the curve. In this paper, we study an explicit set of…