Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups

2009/02/01 by Ingrid Beltiţă, Beltita, Ingrid, Daniel Beltiţă +1
Mathematics · Physics and Astronomy · #22E25 #22E65 #35S05 #47G30 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0902.0148

openalex publication_date 2009/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 grup 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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