Related papers: On local matching property in groups and vector sp…
We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.
The theory of p-local compact groups, developed in an earlier paper by the same authors, is designed to give a unified framework in which to study the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups,…
This paper develops a theory of polynomial maps from commutative semigroups to arbitrary groups and proves that it has desirable formal properties when the target group is locally nilpotent. We apply this theory to solve Waring's Problem…
We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
We formulate the local Langlands conjecture for connected reductive groups over local fields, including the internal parametrization of L-packets using endoscopy.
Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real…
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting…
We define a variant of intersection space theory that applies to many compact complex and real analytic spaces $X$, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to…
We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…
This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…
In the first section of this paper we prove a theorem for the number of columns of a rectangular area that are identical to the given one. In the next section we apply this theorem to derive several combinatorial identities by counting…
In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the…
The dictionary matching problem is to locate occurrences of any pattern among a set of patterns in a given text. Massive data sets abound and at the same time, there are many settings in which working space is extremely limited. We…
A matching in a group G is a bijection f from a subset A to a subset B in G such that af(a) does not belong to A for all a in A. The group G is said to have the matching property if, for any finite subsets A,B in G of same cardinality with…
We examine subgroups of locally compact groups that are continuous homomorphic images of connected Lie groups and we give a criterion for being such an image. We also provide a new characterisation of Lie groups and a characterisation of…
We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…