Journal of Operator Theory

Volume 69, Issue 1, Winter 2013 pp. 33-58.

Magnetic twisted actions on general abelian $C^*$-algebras

Authors: Fabian Belmonte (1), Max Lein (2), and Marius Mantoiu (3)
Author institution: (1) SISSA-ISAS, Via Bonomea, 265, 728, building A, 34136 Trieste, Italy
(2) Eberhard Karls Universitaet Tuebingen, Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany
(3) Dept. de Matematicas, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile

Summary: We introduce magnetic twisted actions of $\mathscr{X}=\mathbb{R}^n$ on general abelian $C^*$-algebras and study the associated twisted crossed product and pseudodifferential algebras in the framework of strict deformation quantization.

Keywords: pseudodifferential calculus, Poisson algebra, crossed product, magnetic field, dynamical system

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