Twisted Pseudo-differential Operators on Type I Locally Compact Groups

2016/05/16 by H. Bustos, Bustos, H., Marius Măntoiu +1
Mathematics · Physics and Astronomy · #22D25 #47G30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Primary 81S30 #Secondary 22D10

paper · pdf · doi:10.48550/arxiv.1605.04961

openalex publication_date 2016/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \G be a locally compact group satisfying some technical requirements and \wG its unitary dual. Using the theory of twisted crossed product C^*-algebras, we develop a twisted global quantization for symbols defined on \G×\wG and taking operator values. The emphasis is on the representation-theoretic aspect. For nilpotent Lie groups, the connection is made with a scalar quantization of the cotangent bundle T^*(\G) and with a Quantum Mechanical theory of observables in the presence of variable magnetic fields.

Related

• Pseudo-differential operators, Wigner transform and Weyl systems on type\n I locally compact groups
• Twisting of the Quantum double and the Weyl algebra
• Full quantum crossed products, invariant measures, and type-I lifting
• Deformation of C*-algebras by cocycles on locally compact quantum groups
• The standard construction for cocycle twisted and braided tensor product W^*-algebras