Related papers: A $P$-Adic Spectral Triple
We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic…
In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.
In this paper, we prove that unital homomorphisms from continuous functions on a compact metric space to matrices over a C*-algebra with tracial rank at most one are approximately diagonalizable. We also consider some generalizations of…
We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf…
We define spectral freeness for actions of discrete groups on C*-algebras. We relate spectral freeness to other freeness conditions; an example result is that for an action of a finite group, spectral freeness is equivalent to strong…
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum…
This paper provides the generating series for the embedding of tree-like graphs of arbitrary number of vertices, accourding to their genus. It applies and extends the techniques of Chan, where it was used to give an alternate proof of the…
We construct discrete versions of $\kappa$-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical…
We present a construction, called the limit of a tree system of spaces (or, less formally, a tree of spaces). The construction is designed to produce compact metric spaces that resemble fractals, out of more regular spaces, such as closed…
Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral…
Explicit formulas are obtained for a family of continuous mappings of p-adic numbers $\Qp$ and solenoids $\Tp$ into the complex plane $\sC$ and the space \~$\Rs ^{3}$, respectively. Accordingly, this family includes the mappings for which…
An invariant for cospectral graphs is a property shared by all cospectral graphs. In this paper, we establish three novel arithmetic invariants for cospectral graphs, revealing deep connections between spectral properties and combinatorial…
The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras, where the continued fraction expansion of $\theta$ encodes the dimensions of the summands,…
We prove that a polynomial path of Riemannian metrics on a closed spin manifold induces a continuous field in the spectral propinquity of metric spectral triples.
We prove new results on generalized derivations on C$^*$-algebras. By considering the triple product $\{a,b,c\} =2^{-1} (a b^* c + c b^* a)$, we introduce the study of linear maps which are triple derivations or triple homomorphisms at a…
A characterization is given for directed graphs that yield graph $C^*$-algebras with continuous trace. This is established for row-finite graphs with no sources first using a groupoid approach, and extended to the general case via the…
In order to extend the spectral action principle to non-compact spaces, we propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. We show that an example is…
The author's recent results on spectral invariant dense subalgebras of C*-algebras associated with dynamical systems are summarized. If G is a compactly generated polynomial growth Type R Lie group, and the action of G on S(M) (Schwartz…
We define variants of Pisier's similarity degree for unital C*-algebras and use direct integral theory to obtain new results. We prove that if every II$_{1}$ factor representation of a separable C*-algebra $\mathcal{A}$ has property…
We obtain new partial results supporting the spectral set conjecture in dimension 1.