Results 1 to 10 of about 3,211 (69)

Gysin sequences and SU(2)‐symmetries of C∗‐algebras

Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 440-492, December 2021., 2021
Abstract Motivated by the study of symmetries of C∗‐algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)‐equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz–Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant K‐theory.
Francesca Arici, Jens Kaad
wiley   +1 more source

Injectivity results for coarse homology theories

Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1619-1684, December 2020., 2020
Abstract We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class of linear groups or, more generally, groups with finite decomposition complexity.
Ulrich Bunke, Alexander Engel, Daniel Kasprowski, Christoph Winges   +3 more
wiley   +1 more source

Modified Novikov Operators and the Kastler‐Kalau‐Walze‐Type Theorem for Manifolds with Boundary

Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020
In this paper, we give two Lichnerowicz‐type formulas for modified Novikov operators. We prove Kastler‐Kalau‐Walze‐type theorems for modified Novikov operators on compact manifolds with (respectively without) a boundary. We also compute the spectral action for Witten deformation on 4‐dimensional compact manifolds.
Sining Wei, Yong Wang, John D. Clayton
wiley   +1 more source

Spectral noncommutative geometry and quantization: a simple example [PDF]

, 1999
We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative geometry defined by a spectral triple, and study its quantization.
A. Connes, A. Connes, A. Connes, A. H. Chamseddine, A. H. Chamseddine, B. Iochum, C. Rovelli, Carlo Rovelli, D. Kastler, D. Kastler, D. Kastler, D. Kastler, G. Landi, G. Landi, H. Grosse, H. Grosse, H. Grosse, H. Grosse, J. Lukierski, J. Madore, S. Doplicher, S. Doplicher, S. Doplicher, S. Majid, S. Majid, S. Majid, T. Brzezinski, T. Filk, W. Kalau   +28 more
core   +2 more sources

Gauge Symmetry Breaking in Matrix Models [PDF]

, 2010
We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge theory as well as gravity in an emergent way.
Grosse, Harald, Lizzi, Fedele, Steinacker, Harold   +2 more
core   +1 more source

Noncommutativity in Effective Loop Quantum Cosmology

Advances in High Energy Physics, Volume 2019, Issue 1, 2019., 2019
We construct a noncommutative extension of the Loop Quantum Cosmology effective scheme for the flat FLRW model with a free scalar field via a theta deformation. Firstly, a deformation is implemented in the configuration sector, among the holonomy variable and the matter degree of freedom.
Abraham Espinoza-García, Efraín Torres-Lomas, Sinuhé Pérez-Payán, Luis Rey Díaz-Barrón, Edward Sarkisyan-Grinbaum   +4 more
wiley   +1 more source

Noncommutative Geometry and the standard model with neutrino mixing [PDF]

, 2006
We show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with gravity--into a ...
A. Connes, A. Connes, A. Connes, Alain Connes, L. Da̧browski, M. Knecht, M. Veltman, O. Lauscher, R.N. Mohapatra, S. Coleman   +9 more
core   +2 more sources

On Quantum Statistical Mechanics: A Study Guide

Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017
We provide an introduction to a study of applications of noncommutative calculus to quantum statistical physics. Centered on noncommutative calculus, we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems and their consequences. These include the emergence of algebraic approach and the necessity
Wladyslaw Adam Majewski, Remi Léandre
wiley   +1 more source

Chiral spinors and gauge fields in noncommutative curved space-time [PDF]

, 2002
The fundamental concepts of Riemannian geometry, such as differential forms, vielbein, metric, connection, torsion and curvature, are generalized in the context of non-commutative geometry.
A. Connes, A. Sitarz, A.H. Chamseddine, A.H. Chamseddine, A.H. Chamseddine, C.J. Isham, D. Kastler, G. Landi, J.C. Varilly, Kameshwar C. Wali, M. Dubois-Violette, M.J. Duff, N.A. Viet, N.A. Viet, Nguyen Ai Viet, Nguyen Ai Viet, O. Klein, R. Coquereaux, T. Damour, Th. Kaluza, V.P. Nair, W. Kalau, Y. Thirry   +22 more
core   +2 more sources

On Cluster C⁎‐Algebras

Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016
We introduce a C⁎‐algebra A(x,Q) attached to the cluster x and a quiver Q. If QT is the quiver coming from triangulation T of the Riemann surface S with a finite number of cusps, we prove that the primitive spectrum of A(x,QT) times R is homeomorphic to a generic subset of the Teichmüller space of surface S.
Igor V. Nikolaev, Gelu Popescu
wiley   +1 more source