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In this paper, the authors consider the range of a certain class of ASH algebras in [An, Q., Elliott, G. A., Li, Z. and Liu, Z., The classification of certain ASH C*-algebras of real rank zero, J. Topol. Anal., 14(1), 2022, 183–202], which is under the scheme of the Elliott program in the setting of real rank zero C*-algebras. As a reduction theorem, they prove that all these ASH algebras are still the AD algebras studied in [Dadarlat, M. and Loring, T. A., Classifying C*-algebras via ordered, mod-p K-theory, Math. Ann., 305, 1996, 601–616]. [ABSTRACT FROM AUTHOR]

In this paper, for 1 < p < ∞, the authors show that the coarse ℓp-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu's Property (H). [ABSTRACT FROM AUTHOR]

In this paper, we give a classification of real rank zero C*-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C . [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the propagation of topological currents along magnetic interfaces (also known as magnetic walls) of a two-dimensional material. We consider tight-binding magnetic models associated to generic magnetic multi-interfaces and describe the K -theoretical setting in which a bulk-interface duality can be derived. Then, the (trivial) case of a localized magnetic field and the (non trivial) case of the Iwatsuka magnetic field are considered in full detail. This is a pedagogical preparatory work that aims to anticipate the study of more complicated multi-interface magnetic systems. [ABSTRACT FROM AUTHOR]

In the setting of non-type II 1 representations, we propose a definition of deformed Fredholm module [ D T | D T | - 1 , · ] T for a modular spectral triple T , where D T is the deformed Dirac operator. D T is assumed to be invertible for the sake of simplicity, and its domain is an “essential” operator system E T . According to such a definition, we obtain [ D T | D T | - 1 , · ] T = | D T | - 1 d T (·) + d T (·) | D T | - 1 , where d T is the deformed derivation associated to D T . Since the “quantum differential” 1 / | D T | appears in a symmetric position, such a definition of Fredholm module differs from the usual one even in the undeformed case, that is in the tracial case. Therefore, it seems to be more suitable for the investigation of noncommutative manifolds in which the nontrivial modular structure might play a crucial role. We show that all models in Fidaleo and Suriano (J Funct Anal 275:1484–1531, 2018) of non-type II 1 representations of noncommutative 2-tori indeed provide modular spectral triples, and in addition deformed Fredholm modules according to the definition proposed in the present paper. Since the detailed knowledge of the spectrum of the Dirac operator plays a fundamental role in spectral geometry, we provide a characterisation of eigenvalues and eigenvectors of the deformed Dirac operator D T in terms of the periodic solutions of a particular class of eigenvalue Hill equations. [ABSTRACT FROM AUTHOR]

We discuss various aspects of noncommutative geometry of smooth subalgebras of Bunce-Deddens-Toeplitz algebras. [ABSTRACT FROM AUTHOR]

We show that the following properties of the C*-algebras in a class P are inherited by simple unital C*-algebras in the class of asymptotically tracially in P : (1) n-comparison, (2) α-comparison (1 ≤ α < ∞). [ABSTRACT FROM AUTHOR]

We show that if a countable discrete group acts properly and isometrically on a spin manifold of bounded Riemannian geometry and uniformly positive scalar curvature, then, under a suitable condition on the group action, the maximal higher index of the Dirac operator vanishes in K-theory of the maximal equivariant Roe algebra. The group action is not assumed to be cocompact. A key step in the proof is to establish a functional calculus for the Dirac operator in the maximal equivariant uniform Roe algebra. This allows us to prove vanishing of the index of the Dirac operator in K-theory of this algebra, which in turn yields the result for the maximal higher index. [ABSTRACT FROM AUTHOR]

We give a proof of the index theorem of lattice Wilson–Dirac operators, which states that the index of a twisted Dirac operator on the standard torus is described in terms of the corresponding lattice Wilson–Dirac operator. Our proof is based on the higher index theory of almost flat vector bundles. [ABSTRACT FROM AUTHOR]

In this article, we present a trichotomy (a division into three classes) on Noetherian and Artinian C*-algebras and obtain some structural results about Noetherian (and/or Artinian) C*-algebras. We show that every Noetherian, purely infinite and σ-unital C*-algebra A is generated as a C*-ideal by a single projection. We show that if A is a purely infinite, nuclear, separable, Noetherian and Artinian C*-algebra, then A ≅ A ⊗ Z ≅ A ⊗ O ∞ . This is a partial extension of Kirchberg's O ∞ -absorption theorem and Kirchberg's exact embedding theorem. Finally, we show that each Noetherian AF-algebra has a full finite-dimensional C*-subalgebra. [ABSTRACT FROM AUTHOR]