Abstract
We develop a pseudo-differential Weyl calculus on nilpotent Lie groups, which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose, we investigate an infinite-dimensional Lie group constructed as the semidirect product of a nilpotent Lie group and an appropriate function space thereon. We single out an appropriate coadjoint orbit in the semidirect product and construct our pseudo-differential calculus as a Weyl quantization of that orbit.
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