Related papers: Etale groupoids and their quantales
Our aim is to precisely present a tame topology counterpart to canonical stratification of a Lie groupoid. We consider a definable Lie groupoid in semialgebraic, subanalytic, o-minimal over $\mathbb{R}$, or more generally, Shiota's…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
A version of the tangential LS category is introduced for topological laminations with a transverse invariant measure. Here, we use the transverse measure of the contraction of a tangential categorical open set instead of counting this set.…
This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…
We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…
We define extensions of the $L^2$-analytic invariants of closed manifolds, called delocalized $L^2$-invariants. These delocalized invariants are constructed in terms of a nontrivial conjugacy class of the fundamental group. We show that in…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
We call a unital locally convex algebra $A$ a continuous inverse algebra if its unit group $A^\times$ is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group $G$ on a…
Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative, more algebraic construction in the special case of a topos…
We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of point sets which are obtained by a cut and projection scheme…
A magmoid is a non-empty set with a partial binary operation; group-like magmoids generalize group-like magmas such as semigroups, monoids and groups. In this article, we first consider the many ways in which the notions of associative…
This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative…
The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class…
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
We define a quandle variety as an irreducible algebraic variety $Q$ endowed with an algebraically defined quandle operation $\rhd$. It can also be seen as an analogue of a generalized affine symmetric space or a regular $s$-manifold in…
A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a globalization. This result is used to establish a connection between ordered partial actions of groupoids and a multi-object analogue…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…