Related papers: On k-decomposability of positive maps
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic…
We present a general scheme that allows for construction of scalar separability criteria from positive but not completely positive maps. The concept is based on a decomposition of every positive map $\Lambda$ into a difference of two…
We give a unifying description of all inequivalent vector bundles over the 2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via equivariant maps. Each projector determines the projective module of finite type of…
The new paper will be submitted.
In this paper, we discuss positive maps induced by (irreducibly) covariant linear operators for finite groups. The application of group theory methods allows deriving some new results of a different kind. In particular, a family of…
Given a toric degeneration (a degeneration to a toric variety), over the complex numbers, we construct a surjective continuous map from a general fiber to the special fiber of the degeneration in the classical topology. The construction is…
We develop a theory of modulus sheaves with transfers, which generalizes Voevodsky's theory of sheaves with transfers. This paper and its sequel are foundational for the theory of motives with modulus, which is developed in [KMSY20].
The Tomita-Takesaki modular theory is used to establish a cluster estimate extending and modifying that of Thomas and Wichmann, so as to extend it to regions within which the relevant observables are not necessarily spacelike separated.…
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…
We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.
In this paper, we continue the program initiated by Kahn-Saito-Yamazaki by constructing and studying an unstable motivic homotopy category with modulus, extending the Morel-Voevodsky construction from smooth schemes over a field $k$ to…
Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a sufficient condition for a positive map to be exposed. This is an analog of a spanning property which guaranties that a positive map is optimal.…
The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to…
We study mapping cones and their dual cones of positive maps of the n by n matrices into itself. For a natural class of cones there is a close relationship between maps in the cone, super-positive maps, and separable states. In particular…
The paper is a short survey of recent developments in the area of word maps evaluated on groups and algebras. It is aimed to pose questions relevant to Kac--Moody theory.
Kobayashi-Ochiai's theorem says us that the set of dominant rational maps to a complex variety of general type is finite. In this paper, we give a generalization of it in the category of log schemes.