Related papers: Spectral Triples for nonarchimedean local fields

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…

Recently, we found the supersymmetric counterpart of the spectral triple. When we restrict the representation space to the fermionic functions of matter fields, the counterpart which we name "the triple" reduces to the original spectral…

The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schr\"odinger operators with a $\delta$-potential. These operators arise by replacing…

In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the…

Let $R$ be a noetherian ring, $\fa$ an ideal of $R$, $M$ an $R$--module and $n$ a non-negative integer. In this paper we first will study the finiteness properties of the kernel and the cokernel of the natural map $f:\Ext^n_{R}(R/\fa,M)\lo…

We investigate the relations between the (completely bounded) local Coulhon-Varopoulos dimension and the spectral dimension of spectral triples associated to sub-Markovian semigroups (or Dirichlet forms) acting on classical (or…

Given a graph $E$, an action of a group $G$ on $E$, and a $G$-valued cocycle $\phi$ on the edges of $E$, we define a C*-algebra denoted ${\cal O}_{G,E}$, which is shown to be isomorphic to the tight C*-algebra associated to a certain…

We give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

We show that if K is a compact spectrahedron whose set of extreme points is closed, then the operator system of continuous affine functions on K is hyperrigid in the C*-algebra C(ex(K)).

We consider a class of dynamical systems with compact non abelian groups that include C*-, W*- and multiplier dynamical systems. We prove results that relate the algebraic properties such as simplicity or primeness of the fixed point…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have…

We describe a general technique to study Dirac operators on noncommutative spaces under some additional assumptions. The main idea is to capture the compact resolvent condition in a combinatorial set up. Using this, we then prove that for a…

We give sufficient conditions for the presence of the absolutely continuous spectrum of a Schr\"odinger operator on a regular rooted tree without loops (also called regular Bethe lattice or Cayley tree).

We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal…

In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose $G_1, G_2, G_3, \ldots$ is a sequence of finite and connected graphs that share a common universal cover $T$ and such that…

A regular operator T on a Hilbert C^*-module is defined just like a closed operator on a Hilbert space, with the extra condition that the range of (I+T^*T) is dense. Semiregular operators are a slightly larger class of operators that may…

In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ``closed fibers at infinity''. Manin described the dual graph of any such closed fiber in terms of…

In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph $\Lambda$, via the infinite path space $\Lambda^\infty$ of $\Lambda$. Moreover, we prove that this spectral triple has a close…

We introduce to spectral noncommutative geometry the notion of tangled spectral triple, which encompasses the anisotropies arising in parabolic geometry as well as the parabolic commutator bounds arising in so-called "bad Kasparov…