Related papers: type III representations and modular spectral trip…

Noncommutative tori with real multiplication are the irrational rotation algebras that have special equivalence bimodules. Y. Manin proposed the use of noncommutative tori with real multiplication as a geometric framework for the study of…

This note concerns the still open question of representability of Noetherian PI-algebras. Extending a result of Rowen and Small (with an observation of Bergman) that every finitely generated module over a commutative Noetherian ring…

We focus on 4D $\mathcal{N}=2$ string vacua described both by perturbative Heterotic theory and by Type IIA theory; a Calabi--Yau three-fold $X_{\rm IIA}$ in the Type IIA language is further assumed to have a regular K3-fibration. It is…

We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar…

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…

Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an…

To any action of a locally compact group $G$ on a pair $(A,B)$ of von Neumann algebras is canonically associated a pair $(\pi\_A^{\alpha}, \pi\_B^{\alpha})$ of unitary representations of $G$. The purpose of this paper is to provide results…

Let $\mathcal {A}$ be a unital $\ast$-algebra. For $A, B\in\mathcal{A}$, define by $[A, B]_{*}=AB-BA^{\ast}$ and $A\bullet B=AB+BA^{\ast}$ the new products of $A$ and $B$. In this paper, under some mild conditions on $\mathcal {A}$, it is…

We present a spectral triple for $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra. The…

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply…

Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has…

New type III and type N approximate solutions which are regular in the linear approximation are shown to exist. For that, we use complex transformations on self-dual Robinson-Trautman metrics rather then the classical approach. The…

Given a C*-algebra A with a semicontinuous semifinite trace tau acting on the Hilbert space H, we define the family R of bounded Riemann measurable elements w.r.t. tau as a suitable closure, a la Dedekind, of A, in analogy with one of the…

We discuss some properties of the spectral triple $(A_F,H_F,D_F,J_F,\gamma_F)$ describing the internal space in the noncommutative geometry approach to the Standard Model, with $A_F=\mathbb{C}\oplus\mathbb{H}\oplus M_3(\mathbb{C})$. We show…

We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…

We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the…

We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. The algebra, which is assumed to be…

In this thesis, we studied certain mathematical issues related to the computation of the Chamseddine--Connes spectral action on some fundamental noncommutative spectral triples, such as the noncommutative torus and the quantum 3-sphere…

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. Under deformation by a torus action, a standard formula…

The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 1/2 in a magnetic field and an external potential. A new Lieb-Thirring type inequality on the sum of the negative eigenvalues is presented. The main…