Related papers: Groups which are metrically LEF

Let a compact Lie group act ergodically on a unital $C^*$-algebra $A$. We consider several ways of using this structure to define metrics on the state space of $A$. These ways involve length functions, norms on the Lie algebra, and Dirac…

We consider endomorphism actions of arbitrary discrete semigroups on a connected metrizable topological group G. We give necessary and sufficient conditions for expansiveness of such actions when G is a Lie group or a compact…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

Word embeddings are a powerful approach for analyzing language, and exponential family embeddings (EFE) extend them to other types of data. Here we develop structured exponential family embeddings (S-EFE), a method for discovering…

We are interested in classifying groups of local biholomorphisms (or even formal diffeomorphisms) that can be endowed with a canonical structure of algebraic group up to add extra formal diffeomorphisms. We show that this is the case for…

A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of…

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…

By a recent result of Juh\'{a}sz and van Mill, a locally compact topological group whose dense subspaces are all separable is metrizable. In this note we investigate the following question: is every locally compact group having all dense…

We provide a necessary and sufficient condition for the embeddability of a metrizable group into semigroup compactifications associated to uniformly continuous functions. Our result employs a technique used by I. Ben Yaacov, A. Berenstein…

We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and…

In this work we consider interval metrics on groups; that is, integral invariant metrics whose associated weight functions do not have gaps. We give conditions for a group to have and to have not interval metrics. Then we study Lee metrics…

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

Researchers have recently suggested that models share common representations. In our work, we find numerous geometric similarities across the token embeddings of large language models. First, we find ``global'' similarities: token…

The framework developed in the present paper provides a formal ground to generate and study explainable categorizations of sets of entities, based on the epistemic attitudes of individual agents or groups thereof. Based on this framework,…

We explore the ability of word embeddings to capture both semantic and morphological similarity, as affected by the different types of linguistic properties (surface form, lemma, morphological tag) used to compose the representation of each…

We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simple group also has a computable left-order. We also obtain a…

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…

Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study…

We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite and infinite symmetric groups, linear groups, and interval…