The logical quantization of algebraic groups
type: Item
instance of: scholarly article
title: The logical quantization of algebraic groups
zbMATH Open document ID: 0846.18004
DOI: 10.1007/BF00671015
author: Hirokazu Nishimura
published in: International Journal of Theoretical Physics
publication date: 1996-09-22T00:00:00Z
review text: These two papers [see also the following one] are a continuation of the work of the author, begun in the papers ``Manuals in orthogonal categories'' [ibid. 34, No. 2, 211-228 (1995; Zbl 0830.18004)] and ``Empirical sets'' [ibid. 34, No. 2, 229-252 (1995; Zbl 0830.18005)]. The author has a program to develop mathematics in a particular categorical setting, which can be viewed as generalizing Boolean topos theory. The starting points are the notions of a manual of Boolean locales and that of an orthogonal category, as well as the concomitant notion of empirical set, which involves the assignment to each Boolean locale in the manual a sheaf over it. Using this general framework, the author looks at algebraic groups and then differential geometry in the spirit of smooth topoi. The intent is that this approach presents the ``quantized'' or ``Booleanized'' versions. It would probably be useful for the reader to first be exposed to the earlier papers where more of the technical details regarding the underpinnings of this theory can be found.
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 14L99
zbMATH DE Number: 792882
zbMATH Keywords: sheaves
zbMATH Keywords: logical quantization
zbMATH Keywords: Boolean topos theory
zbMATH Keywords: orthogonal category
zbMATH Keywords: empirical set
zbMATH Keywords: Boolean locale
zbMATH Keywords: manual
zbMATH Keywords: algebraic groups
zbMATH Keywords: differential geometry
zbMATH Keywords: smooth topoi
reviewed by: K. I. Rosenthal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 792882