相关论文: Algebraic localization of generalized Wannier base…

Recently, M. Ludewig and G. C. Thiang introduced a notion of a uniformly localized Wannier basis with localization centers in an arbitrary uniformly discrete subset $D$ in a complete Riemannian manifold $X$. They show that, under certain…

We investigate the localization properties of gapped periodic quantum systems, modeled by a periodic or covariant family of projectors, as e.g. the orthogonal projectors on the occupied orbitals at fixed crystal momentum for a gas of…

We generalize Prodan's construction of radially localized generalized Wannier bases [E. Prodan, On the generalized Wannier functions. J. Math. Phys. 56(11), 113511 (2015)] to gapped quantum systems without time-reversal symmetry, including…

We investigate the relation between the localization of generalized Wannier bases and the topological properties of two-dimensional gapped quantum systems of independent electrons in a disordered background, including magnetic fields, as in…

The goal of this paper is to study when uniform Roe algebras have certain $C^*$-algebraic properties in terms of the underlying space: in particular, we study properties like having stable rank one or real rank zero that are thought of as…

We generalize all known results on rigidity of uniform Roe algebras to the setting of arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between uniform Roe algebras of uniformly locally finite coarse…

We provide a construction of Roe (C*-)algebras of general coarse spaces in terms of coarse geometric modules. This extends the classical theory of Roe algebras of metric spaces and gives a unified framework to deal with either uniform or…

We establish a genericity property in the representation theory of a flat family of finite-dimensional algebras in the sense of Cline-Parshal-Scott. More precisely, we show that the decomposition matrices as introduced by Geck and Rouquier…

Let $k$ be an arbitrary field. We construct examples of regular local $k$-algebras $R$ (of positive dimension) for which the ring of differential operators $D_k(R)$ is trivial in the sense that it contains {\it no} operators of positive…

Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown. The first one states that a generic algebraic vector field of degree $d\geq 2$ on the affine…

This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…

We propose a quantization of coarse spaces and uniform Roe algebras. The objects are based on the quantum relations introduced by N. Weaver and require the choice of a represented von Neumann algebra. In the case of the diagonal inclusion…

The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…

In this paper we show that each non-zero ideal of a twisted generalized Weyl algebra (TGWA) $A$ intersects the centralizer of the distinguished subalgebra $R$ in $A$ non-trivially. We also provide a necessary and sufficient condition for…

The rigidity problem for uniform Roe algebras was recently positively solved. Before its solution was found, there were positive solutions under the assumption of certain technical geometric conditions. In this paper, we introduce weaker…

A well-known theorem of W. Fischer and H. Grauert states that analytic fiber spaces with all fibers isomorphic to a fixed compact connected complex manifold are locally trivial. Motivated by this result, we show that if $k$ is an…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. The mixed characteristic case of the conjecture is widely open. We consider the…

Weighted projective space arises when we consider the usual geometric definition for projective space and allow for non-trivial weights. On its own, this extra freedom gives rise to more than enough interesting phenomena, but it is the fact…

We present a mathematical structure which unifies mathematical structures of general relativity and quantum mechanics. It consists of the noncommutative algebra of compactly supported, complex valued functions ${\mathcal A}$, with…

We introduce the concept of Roe C*-algebra for a locally compact groupoid whose unit space is in general not compact, and that is equipped with an appropriate coarse structure and Haar system. Using Connes' tangent groupoid method, we…