Related papers: The injective spectrum of a noncommutative space

We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of this space and detect the spectrality of some of them.

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

For a Veech surface (x,\omega), we characterize subspaces of X^n, invariant under the diagonal action of the affine group of X. We prove that non-arithmetic Veech surfaces have only finitely many invariant subspaces of very particular shape…

In this study, we aim to introduce the concept of a 1-absorbing prime submodule of an unital module over a commutative ring with a non-zero identity. Let M be an R-module and N be a proper submodule of M. For all non-unit elements a, b in R…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…

In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant…

Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…

We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…

With this work we initiate a study of the representations of a unipotent group over a field of characteristic zero from the modular point of view. Let $G$ be such a group. The stack of all representations of a fixed finite dimension $n$ is…

The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are discussed.

The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…

The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The…

Understanding internal representations of neural models is a core interest of mechanistic interpretability. Due to its large dimensionality, the representation space can encode various aspects about inputs. To what extent are different…

A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…

Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…

Here we continue to characterize a recently introduced notion, le-modules $_{R}M$ over a commutative ring $R$ with unity \cite{Bhuniya}. This article introduces and characterizes Zariski topology on the set $Spec(M)$ of all prime submodule…

A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…

We introduce a notion of the noncommutative integrability within a framework of contact geometry.