Open Access
Summer 2016 Twisted pseudo-differential operator on type I locally compact groups
H. Bustos, M. Măntoiu
Illinois J. Math. 60(2): 365-390 (Summer 2016). DOI: 10.1215/ijm/1499760013

Abstract

Let $\mathsf{G}$ be a locally compact group satisfying some technical requirements and $\widehat{\sf{G}}$ its unitary dual. Using the theory of twisted crossed product $C^{*}$-algebras, we develop a twisted global quantization for symbols defined on $\mathsf{G}\times\widehat{\sf{G}}$ 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 $T^{*}(\mathsf{G})$ and with a Quantum Mechanical theory of observables in the presence of variable magnetic fields.

Citation

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H. Bustos. M. Măntoiu. "Twisted pseudo-differential operator on type I locally compact groups." Illinois J. Math. 60 (2) 365 - 390, Summer 2016. https://doi.org/10.1215/ijm/1499760013

Information

Received: 18 July 2016; Revised: 31 August 2016; Published: Summer 2016
First available in Project Euclid: 11 July 2017

zbMATH: 1368.81115
MathSciNet: MR3680539
Digital Object Identifier: 10.1215/ijm/1499760013

Subjects:
Primary: 47G30 , 81S30
Secondary: 22D10 , 22D25

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

Vol.60 • No. 2 • Summer 2016
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