Search
Search Results
-
Twisted Reality and the Second-Order Condition
An interesting feature of the finite-dimensional real spectral triple ( A , H , D , J ) of the Standard Model is that it satisfies a “second-order”...
-
Twisted Reality Condition for Dirac Operators
Motivated by examples obtained from conformal deformations of spectral triples and a spectral triple construction on quantum cones, we propose a new...
-
Curvature of the Determinant Line Bundle for the Noncommutative Two Torus
We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen’s original...
-
Noncommutative Minimal Surfaces
We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass...
-
Noncommutative Galois Extension and Graded q-Differential Algebra
We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q -differential...
-
Twisted Spectral Triple for the Standard Model and Spontaneous Breaking of the Grand Symmetry
Grand symmetry models in noncommutative geometry, characterized by a non-trivial action of functions on spinors, have been introduced to generate...
-
The Geometry of Quantum Lens Spaces: Real Spectral Triples and Bundle Structure
We study almost real spectral triples on quantum lens spaces, as orbit spaces of free actions of cyclic groups on the spectral geometry on the...
-
Modules Over the Noncommutative Torus and Elliptic Curves
Using the Weil–Brezin–Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss...
-
Real Structures on Almost-Commutative Spectral Triples
We refine the reconstruction theorem for almost-commutative spectral triples to a result for real almost-commutative spectral triples, clarifying in...
-
Morita “Equivalences” of Equivariant Torus Spectral Triples
In general, Morita equivalence of spectral triples need not be a symmetric relation. In this paper, we show that Morita equivalence of spectral...
-
On Pythagoras Theorem for Products of Spectral Triples
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes’ distance,...
-
Metric Properties of the Fuzzy Sphere
The fuzzy sphere, as a quantum metric space, carries a sequence of metrics which we describe in detail. We show that the Bloch coherent states, with...
-
A Reconstruction Theorem for Almost-Commutative Spectral Triples
We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner...
-
D-bar Operators on Quantum Domains
We study the index problem for the d-bar operators subject to Atiyah- Patodi-Singer boundary conditions on noncommutative disk and annulus.
-
Connes–Landi Deformation of Spectral Triples
We describe a way to deform a spectral triple with a 2-torus action parametrized by a real deformation parameter, motivated by the Connes–Landi...
-
A Dirac Type Operator on the Non-Commutative Disk
We study an example of the index problem for a Dirac-like operator subject to Atiyah–Patodi–Singer boundary conditions on the noncommutative unit...
-
A C *-Algebraic Model for Locally Noncommutative Spacetimes
Locally noncommutative spacetimes provide a refined notion of noncommutative spacetimes where the noncommutativity is present only for small...
-
Torus Equivariant Spectral Triples for Odd-Dimensional Quantum Spheres Coming from C *-Extensions
The torus group ( S 1 ) ℓ+1 has a canonical action on the odd-dimensional sphere S
q 2ℓ+1 . We take the natural Hilbert space representation where this... -
Gravity and the Noncommutative Residue for Manifolds with Boundary
We prove a Kastler–Kalau–Walze type theorem for the Dirac operator and the signature operator for 3,4-dimensional manifolds with boundary. As a...