Related papers: Elekes-Szab\'o for groups, and approximate subgrou…
A simple proof of the fact that each rank-one infinite measure preserving (i.m.p.) transformation is subsequence weakly rationally ergodic is found. Some classes of funny rank-one i.m.p. actions of Abelian groups are shown to be subsequence…
A topological group is (openly) almost-elliptic if it contains a(n open) dense subset of elements generating relatively-compact cyclic subgroups. We classify the (openly) almost-elliptic connected locally compact groups as precisely those…
We prove a graded version of Alev-Polo's rigidity theorem: the homogenization of the universal enveloping algebra of a semisimple Lie algebra and the Rees ring of the Weyl algebras $A_n(k)$ cannot be isomorphic to their fixed subring under…
We study the groups $G$ with the curious property that there exists an element $k\in G$ and a function $f\colon G\to G$ such that $f(xk)=xf(x)$ holds for all $x\in G$. This property arose from the study of near-rings and input-output…
For an element $g$ of a group $G$, an Engel sink is a subset ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$. A~finite group is nilpotent if and only if…
We prove a weak form of the mean ergodic theorem for actions of amenable locally compact quantum groups in the von Neumann algebra setting.
We define Lie subalgebras of the group algebra of a finite pseudo-reflection group that are involved in the definition of the Cherednik KZ-systems, and determine their structure. We provide applications for computing the Zariski closure of…
By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that hyperbolic groups…
We study the strong, weak, and special amalgamation bases in the varieties of nilpotent groups of class two and exponent n, where n is odd. The main result is a characterization of the special amalgamation bases for these varieties. We also…
A finitely presented group is weakly geometrically simply connected (wgsc) if it is the fundamental group of some compact polyhedron whose universal covering is wgsc i.e. it has an exhaustion by compact connected and simply connected…
A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…
We present sufficient conditions to have global hypoellipticity for a class of Vekua-type operators defined on a compact Lie group. When the group has the property that every non-trivial representation is not self-dual we show that these…
In this paper we determine the precise extent to which the classical sl_2-theory of complex semisimple finite-dimensional Lie algebras due to Jacobson--Morozov and Kostant can be extended to positive characteristic. This builds on work of…
The complete algebraic structure of semisimple finite group algebra of a generalized strongly monomial group is provided. This work extends the work of Broche and del R{\'{\i}}o on strongly monomial groups. The theory is complimented by an…
A well-known theorem of P. Hall, usually called Hall's criterion for nilpotence, states: a group G is nilpotent whenever it has a normal subgroup N such that G/[N,N] and N are nilpotent. We widely generalize this result, replacing groups…
We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…
The Chermak-Delgado lattice of a finite group $G$ is a self-dual sublattice of the subgroup lattice of $G$. In this paper, we focus on finite groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$-group. We…
It is shown that the Ellis semigroup of a $\mathbb Z$-action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with…
A special case of a conjecture raised by Forrest and Runde (Math. Zeit., 2005) asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was aleady known to hold in the non-abelian compact…
Let $\M$ be a von Neumann algebra with a faithful normal trace $\T$, and let $H^\infty$ be a finite, maximal, subdiagonal algebra of $\M$. Fundamental theorems on conjugate functions for weak$^*$\!-Dirichlet algebras are shown to be valid…