Laplace-Beltrami Operators on Noncommutative Tori
Operator Algebras
2020-01-09 v2 Differential Geometry
Abstract
In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian manifolds. The construction takes into account the non-triviality of the group of modular automorphisms. On the way we introduce notions of Riemannian density and Riemannian volumes for noncommutative tori.
Keywords
Cite
@article{arxiv.1905.09048,
title = {Laplace-Beltrami Operators on Noncommutative Tori},
author = {Hyunsu Ha and Raphael Ponge},
journal= {arXiv preprint arXiv:1905.09048},
year = {2020}
}
Comments
v2: typos have been fixed. New normalization of Riemannian volume. To appear in J. Geom. Phys., 28 pages