相关论文: Measuring comodules - their applications

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…

For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…

We study measurements on various subsystems of the output of a universal 1 to 2 cloning machine, and establish a correspondence between these measurements at the output and effective measurements on the original input. We show that one can…

We study the universal measuring coalgebras P(A,B) of Sweedler and the universal measuring comodules Q(M,N) of Batchelor. We show that these universal objects exist in a very general context. We provide a detailed proof of an observation of…

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated…

For measuring families of curves, or, more generally, of measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper \cite{ADS}, Ambrosio, Di Marino and Savar\'e proved that…

A loop is a rather general algebraic structure that has an identity element and division, but is not necessarily associative. Smooth loops are a direct generalization of Lie groups. A key example of a non-Lie smooth loop is the loop of unit…

In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…

Measuring entanglement is a demanding task that usually requires full tomography of a quantum system, involving a number of observables that grows exponentially with the number of parties. Recently, it was suggested that adding a single…

A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…

Recent work of the author established dual representation theorems for certain vector spaces that arise in an important article of Allcock and Vaaler. These results constructed an object called a consistent map which acts like a measure on…

We consider three types of entities for quantum measurements. In order of generality, these types are: observables, instruments and measurement models. If $\alpha$ and $\beta$ are entities, we define what it means for $\alpha$ to be a part…

Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with…

The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…

We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…

Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…

This article includes a survey of the historical development and theoretical structure of the pre-modern theory of magnitudes and numbers. In Part 1, work, insights and controversies related to quantity calculus from Euler onward are…

Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…

Clustering in high dimension spaces is a difficult task; the usual distance metrics may no longer be appropriate under the curse of dimensionality. Indeed, the choice of the metric is crucial, and it is highly dependent on the dataset…

Let $\mathbb{k}$ be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of $\mathbb{k}$. That is, the $\infty$-category of…