Related papers: Some Remarks on Groups with Action on Itself

We define the action of a locally compact group $G$ on a topological graph $E$. This action induces a natural action of $G$ on the $C^*$-correspondence ${\mathcal H}(E)$ and on the graph $C^*$-algebra $C^*(E)$. If the action is free and…

Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…

We determine all finite maximal elementary abelian group actions on compact oriented surfaces of genus $\sigma\geq 2$ which are unique up to topological equivalence. For certain special classes of such actions, we determine group extensions…

We investigate the configuration where a group of finite Morley rank acts definably and generically $m$-transitively on an elementary abelian $p$-group of Morley rank $n$, where $p$ is an odd prime, and $m\geqslant n$. We conclude that…

We classify outer actions (or $\mathscr{G}$-kernels) of discrete amenable groupoids on injective factors. Our method based on unified approach for classification of discrete amenable groups actions, and cohomology reduction theorem of…

In this paper, we prove a Galois correspondence for compact group actions on C*-algebras in the presence of a commuting minimal action. Namely, we show that there is a one to one correspondence between the C*-subalgebras that are globally…

A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {\`a} points fixes") if any element of G has at least one fixed point in X. The G group is said with a common fixed point…

We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.

We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.

We describe the autotopism group Atp(G) of any abelian group G as being a semidirect product of its automorphism group Aut(G) and G^2. We then provide the subgroup structure of Atp(G) when G is a finite cyclic group.

In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].

The small $x$ behaviour of the structure function $h_1(x,Q^2)$ is studied within the leading logarithmic approximation of perturbative QCD. There are two contributions relevant at small $x$. The leading one behaves like $(\frac{1}{x})^0$…

We define the decomposition property for partial actions of discrete groups on $C^*$-algebras. Decomposable partial systems appear naturally in practice, and many commonly occurring partial actions can be decomposed into partial actions…

In this article we develop a notion of soficity for actions of countable groups on sets. We show two equivalent perspectives, several natural properties and examples. Notable examples include arbitrary actions of both amenable groups and…

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

Let $X$ be the $2$-sphere $\mathbb S^2$ or the real projective plane $\mathbb {RP}^2$. We show that if $\Gamma$ is a finitely generated group acting minimally and distally on $X$, then $\Gamma$ contains a nonabelian free subgroup.

Let $K$ be a compact metrizable group and $\Ga$ be a group of automorphisms of $K$. We first show that each $\ap \in \Ga$ is distal on $K$ implies $\Ga$ itself is distal on $K$, a local to global correspondence provided $\Ga$ is a…

We present two examples of actions of non-regular locally compact quantum groups on their homogeneous spaces. The homogeneous spaces are defined in a way specific to these examples, but the definitions we use have the advantage of being…

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…