Related papers: Weak action representability of 2-nilpotent groups

In this paper we investigate relations between Koopman, groupoid and quasi-regular representations of countable groups. We show that for an ergodic measure class preserving action of a countable group G on a standard Borel space the…

Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…

We consider the group $\mathfrak{X}(G)$ obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from…

Consider a lattice $\Gamma$ in a group $G = SL_2(\R), SO(1,n), SU(1,n)$, $SL_2(\Q_p)$. We discuss actions of $\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its…

An \textit{algebraic} action of a discrete group $\Gamma $ is a homomorphism from $\Gamma $ to the group of continuous automorphisms of a compact abelian group $X$. By duality, such an action of $\Gamma $ is determined by a module…

Let $\Gamma$ be a discrete countable group. Consider the crossed product C$^\ast$-algebra $\mathfrak{R}(\Gamma) = C^{\ast}(\Gamma \rtimes l^{\infty}(\Gamma))$. Let $G$ be a larger discrete group, containing $\Gamma$ as an almost normal…

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 show that if G is a discrete group which does not have the Haagerup property but does have an unbounded cocycle into a C_0 representation and if G acts on a finite von Neumann algebra B such that the inclusion B \subset (B \rtimes G) has…

We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact semi-simple Lie groups, but excludes all inner…

Let $\Gamma$ be a finitely generated torsion free nilpotent group, and let $A^\omega$ be the space of infinite words over a finite alphabet $A$. We investigate two types of self-similar actions of $\Gamma$ on $A^\omega$, namely the…

We investigate the behaviour of the Weil character of the symplectic group on restriction to subgroups arising from commutative nilpotent algebras of class 2. We give explicit descriptions of the decomposition of the Weil character when…

We give necessary and sufficient conditions for weak and strong embeddability of amalgams in each subvariety of the category of all nilpotent groups of class at most two; this generalizes B. Maier's result for the latter class. We also…

We introduce a categorical framework for the study of representations of $G_F$, where $G$ is a reductive group, and $\bF$ is a 2-dimensional local field, i.e. $F=K((t))$, where $K$ is a local field. Our main result says that the space of…

Given a $p$-adic group $G$ equipped with an action of a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$, and a reductive fixed-point subgroup $G^\Gamma$, we establish a relationship between constructions of types for these two groups…

We prove that given any compact group G, there exists a minimal action of G on a II_1 factor M such that the bimodule category of the fixed-point II_1 factor M^G is naturally equivalent with the representation category of G. In particular,…

We prove that if $\mathbb A$ is an algebra that is supernilpotent with respect to the $2$-term higher commutator, and $\mathbb B$ is a subalgebra of $\mathbb A$, then $\mathbb B$ is representable as a retract of a finite subdirect power of…

We introduce the definition of totally nonfree actions of groups; such actions are naturally related to the theory of characters of groups and their factor-representations of type II. This short note is a brief exposition of a part of a…

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G…

We give a criterion for the rigidity of actions on homogeneous spaces. Let $G$ be a real Lie group, $\Lambda$ a lattice in $G$, and $\Gamma$ a subgroup of the affine group Aff$(G)$ stabilizing $\Lambda$. Then the action of $\Gamma$ on…

We classify the almost abelian Lie algebras $\mathfrak g_A=\mathbb R e_0 \ltimes_A \mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\in M(2n-1,\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal…