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Quantum and classical pseudogroups. Part I. Union pseudogroups and their quantization

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Abstract

Union pseudogroups (structures analogical to pseudogroups in the sense of [1]) are defined using the category dual to the category of groupoids instead of the category of pseudospaces in the sense of [2]. It is shown that these structures are equivalent to double groups (in the sense of [3]). Moreover, it is shown that a quantization procedure associates with each finite union pseudogroup a (quantum) pseudogroup. Therefore for each finite double group there is a finite pseudogroup.

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  1. Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoza 74, Warszawa, Poland

    S. Zakrzewski

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  1. S. Zakrzewski
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Communicated by H. Araki

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Zakrzewski, S. Quantum and classical pseudogroups. Part I. Union pseudogroups and their quantization. Commun.Math. Phys. 134, 347–370 (1990). https://doi.org/10.1007/BF02097706

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  • DOI: https://doi.org/10.1007/BF02097706

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