Laplace–Beltrami operators on noncommutative tori

Ha, Hyunsu; Ponge, Raphael

doi:10.1016/j.geomphys.2019.103594

Laplace–Beltrami operators on noncommutative tori

May 22, 2019

28 pages

Published in:

J.Geom.Phys. 150 (2020) 103594

Published: Apr, 2020

e-Print:

1905.09048 [math.OA]

DOI:

10.1016/j.geomphys.2019.103594 (publication)

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Abstract: (Elsevier)

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 on noncommutative tori.

Note:

v2: typos have been fixed. New normalization of Riemannian volume. To appear in J. Geom. Phys., 28 pages

Noncommutative tori
Riemannian metrics
Laplace–Beltrami operator

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