Related papers: Simplicial and dimension groups with group action …

For every partially ordered sets I, having a finite cofinal subset, and every field K we build a unital, locally matricial and hence unit-regular K-algebra B(I) such that the lattice of all its ideals is order isomorphic to the lattice of…

A dimension group is a partially ordered countable group such that (1) every finite subset is contained in an ordered subgroup which is a finite direct power of Z and (2) the group has an order unit i.e. a positive element u such that every…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

The notion of chain groups of homeomorphisms of the interval was introduced by Kim, Koberda and Lodha as a generalization of Thompson's group $F$. In this paper, we study an $S^1$-version of chain groups: ring groups. We study the…

We study quantum isometry groups, denoted by $\mathbb{Q}(\Gamma, S)$, of spectral triples on $C^*_r(\Gamma)$ for a finitely generated discrete group coming from the word-length metric with respect to a symmetric generating set $S$. We first…

We introduce the concept of Rokhlin dimension for actions of residually finite groups on C*-algebras, extending previous notions of Rokhlin dimension for actions of finite groups and the integers, as introduced by Hirshberg, Winter and the…

Building on work of Popa, Ioana, and Epstein--T\"{o}rnquist, we show that, for every nonamenable countable discrete group $\Gamma$, the relations of conjugacy, orbit equivalence, and von Neumann equivalence of free ergodic (or weak mixing)…

For a metric space $X$ with a compatible measure $\mu$, Genevois and Tessera defined the Scaling Group of $(X,\mu)$ as the subgroup $\Gamma$ of $\mathbb{R}_{>0}$ of positive real numbers $\gamma$ for which there are quasi-isometries of $X$…

Recently C. Houdayer and Y. Isono have proved among other things that every biexact group $\Gamma$ has the property that for any non-singular strongly ergodic action $\Gamma\curvearrowright (X,\mu)$ on a standard measure space the group…

Let $K$ be a field and $G$ be a finite group. Let $G$ act on the rational function field $K(x(g):g\in G)$ by $K$ automorphisms defined by $g\cdot x(h)=x(gh)$ for any $g,h\in G$. Denote by $K(G)$ the fixed field $K(x(g):g\in G)^G$. Noether's…

Recently Bingbing Liang and Hanfeng Li computed the mean dimension and metric mean dimension for algebraic actions of amenable groups. We show how to extend their computation of metric mean dimension to the case of sofic groups, provided…

We prove that if a countable discrete group $\Gamma$ is {\it w-rigid}, i.e. it contains an infinite normal subgroup $H$ with the relative property (T) (e.g. $\Gamma= SL(2,\Bbb Z) \ltimes \Bbb Z^2$, or $\Gamma = H \times H'$ with $H$ an…

This paper explores the dimension theory of non-Noetherian graded rings by introducing the class of Hilbert-Serre rings. We generalize Krull's dimension theorem and Smoke's dimension theorem by establishing the fundamental inequalities…

Let $G$ be a finite abelian group viewed a $\mathbb{Z}$-module and let $\mathcal{G} = (V, E)$ be a simple graph. In this paper, we consider a graph $\Gamma(G)$ called as a \textit{group-annihilator} graph. The vertices of $\Gamma(G)$ are…

When we consider a finite abelian group acting linearly on a polynomial ring, we can find monomial generators for the subring of invariants. By Noether's degree bound and Hilbert's finiteness theorem, we know that there are finitely many…

We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit of realizability, this is intended to formalize a homotopical…

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a group of isometries of dimension $r$ acting on s-dimensional orbits are obtained. These conditions are Intrinsic, Deductive, Explicit and…

We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonality of morphisms, which we hope might be of use in the…

Given a noetherian local domain $R$ and a valuation $\nu$ of its field of fractions which is non negative on $R$, we derive some very general bounds on the growth of the number of distinct valuation ideals of $R$ corresponding to values…

Let $\Gamma$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\Gamma$ on the circle is either trivial or semi-conjugate to a unique minimal action on the so-called simple circle.