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arXiv · 1605.04961

Twisted Pseudo-differential Operators on Type I Locally Compact Groups

H. Bustos·M. Mantoiu
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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 $\G\times\wG$ 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.

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H. Bustos, M. Mantoiu. 2016-05-16. Twisted Pseudo-differential Operators on Type I Locally Compact Groups. https://arxiv.org/abs/1605.04961

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