Related papers: A note on group actions on subfactors

We prove that a partial action is amenable if and only if so is its Morita enveloping action. As applications we prove that any partial representation of a discrete group is positive definite, and we extend a result of Zeller-Meier…

If $G$ is a countable, discrete group generated by two finite subgroups $H$ and $K$ and $P$ is a II$_1$ factor with an outer G-action, one can construct the group-type subfactor $P^H \subset P \rtimes K$ introduced in \cite{BH}. This…

We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin$^c$-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit…

We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…

Let $H$ be a proper subgroup of a discrete group $G$. We introduce a notion of relative inner amenability of $H$ in $G$, we prove some equivalent conditions and provide examples as well as counter-examples. We also discuss the corresponding…

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We apply the Evans-Kishimoto type argument for centrally free actions of discrete amenable groups on McDuff factors, and classify them. Especially, we present a different proof that the Connes-Takesaki modules are complete cocycle conjugacy…

We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…

We implement GAP functions about groups with action on itself and investigate some basic properties of small groups with action on itself of order $<32$.

We study several stronger versions of sensitivity for minimal group actions, including $n$-sensitivity, thick $n$-sensitivity and blockily thick $n$-sensitivity, and characterize them by the regionally proximal relation.

In this paper, we show that there is a net for amenable transformation groups like F{\o}lner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner…

Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure of the crossed product over the Fourier algebra of the acting group. The resulting characterisation of…

We answer an open question of Grigorchuk and Zuk about amenability using random walks. Our results separate the class of amenable groups from the closure of subexponentially growing groups under the operations of group extension and direct…

We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…

We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…

We introduce and study various notions of amenability continuous (Borel) partial actions of locally compact (Borel) groups $G$ on topological (standard Borel) spaces. We also study amenability of partial representations of a locally compact…

We study hereditary properties of the class of countable groups admitting an amenable, transitive and faithful action on a countable set. We consider mainly the case of amalgamated free products, and we show in particular that the double of…

We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number…