Related papers: Finiteness theorems and algorithms for permutation…

A theory of intrinsic localized modes (ILMs) in anharmonic lattices is developed, which allows one to reduce the original nonlinear problem to a linear problem of small variations of the mode. This enables us to apply the Lifshitz method of…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

We prove that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property we show that almost all finite subsets of the group generate…

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

We provide a simplified characterization of entanglement in physical systems which are symmetric under the action of subgroups of the symmetric group acting on the party labels. Sets of entanglements are inherently equal, lying in the same…

We continue the study of the rich family of norm-closed, automorphism invariant ideals of a continuous nest algebra. First we present a unified framework which captures all stable ideals as the kernels of limits of diagonal compressions. We…

We study semi-stable ideal lattices coming from real quadratic number fields. Specifically, we demonstrate infinite families of semi-stable and unstable ideal lattices of trace type, establishing explicit conditions on the canonical basis…

Let F be a non-archimedean local field of characteristic zero whose residue field has at least three elements. Let G be an almost simple linear algebraic group over F, with rank_F(G) >= 2. Let X be a simply connected symmetric space of…

When a quantum field theory has a symmetry, global or local like in gauge theories, in the tree or classical approximation formal manipulations lead to believe that the symmetry can also be implemented in the full quantum theory, provided…

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…

We demonstrate that the ring of invariants for the natural action of a subgroup G of GL_n(F_q) on a polynomial ring R=K[X_1,...,X_n] need not be F-pure. In these examples G is the symplectic group over a finite field, and the invariant…

We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $\mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists…

The conditions for stability of the elements of linear groups over the associative rings with identity and their connection with the stability of rings are analyzed in the article. The stability of rings which are commutative, satisfy the…

The question of open-loop control in the Gaussian regime may be cast by asking which Gaussian unitary transformations are reachable by turning on and off a given set of quadratic Hamiltonians. For compact groups, including finite…

We prove an operator algebraic superrigidity statement for homomorphisms of irreducible lattices, and also their commensurators, in certain higher-rank groups into unitary groups of finite factors. This extends the authors' previous work…

Unbounded entailment relations, introduced by Paul Lorenzen (1951), are a slight variant of a notion which plays a fundamental r\^ole in logic (see Scott 1974) and in algebra (see Lombardi and Quitt\'e 2015). We call systems of ideals their…

We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes we conclude that every such algebra is normal and Cohen-Macaulay, and give an interpretation of its…

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed…

We study Artin-Schelter Gorenstein fixed subrings of some Artin-Schelter regular algebras of dimension 2 and 3 under finite group actions, and prove a noncommutative version of the Kac-Watanabe and Gordeev theorem for these algebras.

We consider a finite, connected and simple graph $\Gamma$ that admits a vertex-transitive group of automorphisms $G$. Under the assumption that, for all $x \in V(\Gamma)$, the local action $G_x^{\Gamma(x)}$ is the action of…