Related papers: A note on group actions on subfactors

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.

We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular,…

We will show the uniqueness of outer coactions of finite groups on the AFD factor of type II$_1$ along the arguments by Connes, Jones and Ocneanu. Namely, we construct the infinite tensor product type action, adopt it as the model action,…

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if…

We provide an alternative proof for the extreme amenability of the unitary group of the hyperfinite II${}_1$-factor von Neumann algebra, endowed with the strong operator topology.

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…

By combining R{\o}rdam's construction and the author's previous construction, we provide the first examples of amenable actions of non-amenable groups on simple separable nuclear C*-algebras that are neither stably finite nor purely…

Let $G$ be a countable discrete amenable group, ${\cal M}$ a McDuff factor von Neumann algebra, and $A$ a separable nuclear weakly dense C$^*$-subalgebra of ${\cal M}$. We show that if two centrally free actions of $G$ on ${\cal M}$ differ…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

In 2005, Abdollahi and Rejali, studied the relations between paradoxical decompositions and configurations for semigroups. In the present paper, we introduce another concept of amenability on semigroups and groups which includes amenability…

We extend some recent results about bounded invariant equivalence relations and invariant subgroups of definable groups: we show that type-definability and smoothness are equivalent conditions in a wider class of relations than heretofore…

To study outer actions $\a$ of a group $G$ on a factor $\sM$ of type {\threel}, $0<\la<1$, we study first the cohomology group of a group with the unitary group of an abelian {\vna} as a coefficient group and establish a technique to reduce…

We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.

We extend the notion of Novikov-Shubin invariant for free G-CW-complexes of finite type to spaces with arbitrary G-actions and prove some statements about their positivity. In particular we apply this to classifying spaces of discrete…

In this note we study the finite groups whose subgroup lattices are dismantlable.

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…