Related papers: Spin geometry of the rational noncommutative torus

We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…

The spin susceptibility is an important probe to characterize the symmetry of the order parameter in unconventional superconductors. Among them, nonunitary triplet superconductors have attracted a lot of attention recently in the context of…

A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of…

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…

We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…

This article discusses the representation theory of noncommutative algebras reality-based algebras with positive degree map over their field of definition. When the standard basis contains exactly two nonreal elements, the main result…

We refine the reconstruction theorem for almost-commutative spectral triples to a result for real almost-commutative spectral triples, clarifying, in the process, both concrete and abstract definitions of real commutative and…

A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole…

In this work we examine generalized Connes-Lott models on the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure…

We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…

The spectral distance for noncommutative Moyal planes is considered in the framework of a non compact spectral triple recently proposed as a possible noncommutative analog of non compact Riemannian spin manifold. An explicit formula for the…

This paper constructs (with challenging obstacles) on the three torus with its cubical decomposition: Firstly, a combinatorial graded intersection algebra (graded by the codimension) which is commutative and associative defined by…

Spin textures, i.e., the distribution of spin polarization vectors in reciprocal space, exhibit diverse patterns determined by symmetry constraints, resulting in a variety of spintronic phenomena. Here, we propose a universal theory to…

To each non-isotropic almost-complex immersion of a 2-torus into $ S ^ 6 $ we associate an algebraic curve, called the spectral curve, and a linear flow in the intersection of two Prym varieties on this spectral curve. We show that…

In this talk, based on work done in collaboration with G. Landi and R.J Szabo, I will review how string theory can be considered as a noncommutative geometry based on an algebra of vertex operators. The spectral triple of strings is…

The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides the split cases, one for each complex simple Lie algebra, there are two kinds of non-split…

We show how a suitably twisted Spin-cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others.…

Quantum spin rings represent fundamental model systems that exhibit distinctive quantum phenomena-such as quantum critical behavior and quasiparticle excitations-arising from their periodic boundary conditions and enhanced quantum…

First we consider the deformations of superspaces with N=(1,1) and N=(2,2) supersymmetries in two dimensions. Among these the construction of noncommutative supertorus with odd spin structure is possible only in the case of N=(2,2)…

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…