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A locally compact quantum group arising from quantization of the affine group of a local field. (English) Zbl 1411.81117

Summary: Using methods coming from non-formal equivariant quantization, we construct in this short note a unitary dual 2-cocycle on a discrete family of quotient groups of subgroups of the affine group of a local field (which is not of characteristic 2, nor an extension of \(\mathbb{Q}_2\)). Using results of De Commer about Galois objects in operator algebras, we obtain new examples of locally compact quantum groups in the setting of von Neumann algebras.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
81S05 Commutation relations and statistics as related to quantum mechanics (general)
14L17 Affine algebraic groups, hyperalgebra constructions
46L10 General theory of von Neumann algebras
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References:

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