相关论文: Quadratic maps between groups

The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…

In this work, we offer a historical stroll through the vast topic of binary quadratic forms. We begin with a quick review of their history and then an overview of contemporary algebraic developments on the subject.

Quadrance between two points A_1 = [x_1,y_1] and A_2 = [x_2,y_2] is the number Q (A_1, A_2) := (x_2 - x_1)^2 + (y_2 - y_1)^2. In this paper, we present some interesting results arise from this notation. In Section 1, we will study geometry…

We study functional graphs generated by several quadratic polynomials, acting simultaneously on a finite field of odd characteristic. We obtain several results about the number of leaves in such graphs. In particular, in the case of graphs…

Let $\mathsf{Q}$ be a commutative and unital quantale. By a $\mathsf{Q}$-map we mean a left adjoint in the quantaloid of sets and $\mathsf{Q}$-relations, and by a partial $\mathsf{Q}$-map we refer to a Kleisli morphism with respect to the…

As a generalization of orbit-polynomial and distance-regular graphs, we introduce the concept of a quotient-polynomial graph. In these graphs every vertex $u$ induces the same regular partition around $u$, where all vertices of each cell…

There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…

We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…

We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.

This article is the first in a series devoted to computing the class groups of real quadratic fields. We present a new relation between the class number and the index of unit groups. This relation generalizes Hilbert class field theory for…

The (proper) power graph of a group is a graph whose vertex set is the set of all (nontrivial) elements of the group and two distinct vertices are adjacent if one is a power of the other. Various kinds of planarity of (proper) power graphs…

In this article, we prove that every quadratic rational map whose multipliers all lie in the ring of integers of a given imaginary quadratic field is a power map, a Chebyshev map or a Latt\`{e}s map. In particular, this provides some…

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…

We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of…

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…

A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups…

The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; $viz.$ the map $x\mapsto x^M$ for a group $G$, and an integer $M\geq 2$. Here, we accumulate various…

Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…