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Laplace-Beltrami Operators on Noncommutative Tori

Published 22 May 2019 in math.OA and math.DG | (1905.09048v2)

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.

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Authors (2)

  1. Hyunsu Ha 
  2. Raphael Ponge 

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