Related papers: A Class of Noncommutative Spectra

We introduce a class of noncommutative spectra and give the sheaf structure on the class of noncommutative spectra.

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.

We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that…

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…

We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.

For a noncommutative space X, we study Inj(X), the set of isomorphism classes of indecomposable injective X-modules. In particular, we look at how this set, suitably topologized, can be viewed as an underlying "spectrum" for X. As…

We study spectra of noncommutative dynamical systems, representations of fractal groups, and regular graphs. We explicitly compute these spectra for five examples of groups acting on rooted trees, and in three cases obtain totally…

This is a survey of noncommutative generalizations of the spectrum of a ring, written for the Notices of the American Mathematical Society.

A wide class of noncommutative spaces, including 4-spheres based on all the quantum 2-spheres and suspensions of matrix quantum groups is described. For each such space a noncommutative vector bundle is constructed. This generalises and…

The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative algebra.

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…

These notes aim to give an introduction to a few aspects of noncommutative geometry.

These notes give a brief introduction to the category of spectra as defined in stable homotopy theory. In particular, Section 5 discusses an extensive list of examples of spectra whose properties have been found to be interesting.

We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non trivial integrable model.

In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.

We find a class of algebras A satisfying the following property: for every nontrivial noncommutative polynomial, the linear span of all its values in A equals A. This class includes the algebras of all bounded and all compact operators on…

We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…

We present a definition of and discuss basic properties of cross-ratios over noncommutative skew-fields. A new theorem was added.

In this paper, as an analogue of the spectrum of a tensor triangulated category introduced by Balmer, we define a spectrum of a triangulated category which does not necessarily admit a tensor structure. We apply it for some triangulated…

In previous papers, we constructed smooth (1,\infty)-summable semfinite spectral triples for graph algebras with a faithful trace, and (k,\infty)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes…