Affine noncommutative geometry - Analyse, géométrie et modélisation Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Affine noncommutative geometry

Teo Banica
  • Fonction : Auteur
  • PersonId : 1045618

Résumé

This is an introduction to noncommutative geometry, from an algebraic and probabilistic viewpoint. We are mostly interested in free geometry, thought to be of help in connection with quantum and statistical mechanics. The spaces $\mathbb R^N,\mathbb C^N$ have no free analogues, but the corresponding unit spheres $S^{N-1}_\mathbb R,S^{N-1}_\mathbb C$ do have free analogues $S^{N-1}_{\mathbb R,+},S^{N-1}_{\mathbb C,+}$, and it is about the submanifolds $X\subset S^{N-1}_{\mathbb R,+},S^{N-1}_{\mathbb C,+}$, chosen algebraic, and of Riemannian flavor, with an integration functional $tr:C(X)\to\mathbb C$, that we will talk about here. We also discuss some other related geometries, called easy, completing the picture formed by the 4 main geometries, namely classical/free, real/complex.
Fichier principal
Vignette du fichier
ng.pdf (1.52 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03312800 , version 1 (02-08-2021)
hal-03312800 , version 2 (16-11-2021)
hal-03312800 , version 3 (14-04-2022)
hal-03312800 , version 4 (31-10-2022)
hal-03312800 , version 5 (02-05-2023)

Identifiants

  • HAL Id : hal-03312800 , version 4

Citer

Teo Banica. Affine noncommutative geometry. 2022. ⟨hal-03312800v4⟩
50 Consultations
117 Téléchargements

Partager

Gmail Facebook X LinkedIn More