English
Related papers

Related papers: On a group associated to $z^2-1$

200 papers

Let $J$ be the Jacobian of a smooth projective curve. We define a natural action of the Lie algebra of polynomial Hamiltonian vector fields on the plane, vanishing at the origin, on the Chow group of $J$ with rational coefficients. Using…

Algebraic Geometry · Mathematics 2007-05-23 Alexander Polishchuk

We consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of their Galois groups as subgroups of…

Number Theory · Mathematics 2020-05-29 Irene I. Bouw , Ozlem Ejder , Valentijn Karemaker

We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert…

Group Theory · Mathematics 2017-10-27 Jérémie Brieussel , Ryokichi Tanaka , Tianyi Zheng

Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…

Algebraic Geometry · Mathematics 2020-02-18 Serge Cantat , Yves de Cornulier

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

Algebraic Geometry · Mathematics 2007-05-23 Ralph M. Kaufmann

The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…

High Energy Physics - Theory · Physics 2015-06-17 Sebastian Franco , Daniele Galloni , Alberto Mariotti

We leverage a correspondence between group actions and edge-labelled graphs in two ways. First, we give a unified presentation of several folklore results connecting weak containment, local-global convergence, and continuous model theory.…

Combinatorics · Mathematics 2024-10-24 Riley Thornton

Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…

Group Theory · Mathematics 2026-04-10 Richard Weidmann , Thomas Weller

This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that, if there exists a Cayley graph with finitely many Busemann points, then the…

Group Theory · Mathematics 2025-11-27 Corentin Bodart , Liran Ron-George , Ariel Yadin

The a-adic numbers are those groups that arise as Hausdorff completions of noncyclic subgroups of the rational numbers. We give a crossed product construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers and investigate…

Operator Algebras · Mathematics 2015-12-15 S. Kaliszewski , Tron Omland , John Quigg

Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least…

Geometric Topology · Mathematics 2007-05-23 Renato Feres , Dave Witte

We construct a model for the space of automorphisms of a connected p-compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer…

Algebraic Topology · Mathematics 2014-11-11 Kasper K. S. Andersen , Jesper Grodal

Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid…

Rings and Algebras · Mathematics 2026-05-27 Josiah Aakre

We study the arithmetic of curves and Jacobians endowed with the action of a finite group $G$. This includes a study of the basic properties, as $G$-modules, of their $\ell$-adic representations, Selmer groups, rational points and…

Number Theory · Mathematics 2024-07-29 Alexandros Konstantinou , Adam Morgan

We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective flat schemes over Z with a tame action of a finite abelian group. This formula…

Number Theory · Mathematics 2007-05-23 T. Chinburg , G. Pappas , M. Taylor

We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the…

Dynamical Systems · Mathematics 2013-12-06 Rich Stankewitz , Hiroki Sumi

A new universal model to implement the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the…

High Energy Physics - Theory · Physics 2014-11-20 Michael Kuchiev

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. In particular, we discuss some important totally geodesic…

Differential Geometry · Mathematics 2017-10-24 Yu. G. Nikonorov

The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of…

Quantum Algebra · Mathematics 2022-03-25 Daniel Gromada

We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…

Dynamical Systems · Mathematics 2018-09-21 Daniel Lenz