Isometric Spectral Subtriples
Mathematical Physics
2024-04-26 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Operator Algebras
Abstract
We investigate the notion of subsystem in the framework of spectral triple as a generalized notion of noncommutative submanifold. In the case of manifolds, we consider several conditions on Dirac operators which turn embedded submanifolds into isometric submanifolds. We then suggest a definition of spectral subtriple based on the notion of submanifold algebra and the already existing notions of Riemannian, isometric, and totally geodesic morphisms. We have shown that our definitions work at least in some relevant almost commutative examples.
Keywords
Cite
@article{arxiv.2404.16332,
title = {Isometric Spectral Subtriples},
author = {Paolo Bertozzini and Wanchalerm Sucpikarnon and Apimook Watcharangkool},
journal= {arXiv preprint arXiv:2404.16332},
year = {2024}
}
Comments
25 pages, LaTeX2e, published paper reformatted for arXiv purposes