Affine noncommutative geometry
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.
Domaines
Algèbres d'opérateurs [math.OA]
Origine : Fichiers produits par l'(les) auteur(s)