Independence of automorphism group, center, and state space of quantum logics
type: Item
instance of: scholarly article
title: Independence of automorphism group, center, and state space of quantum logics
zbMATH Open document ID: 0771.03021
DOI: 10.1007/BF00675085
published in: International Journal of Theoretical Physics
publication date: 1993-01-16T00:00:00Z
review text: Let \(L\) be a quantum logic and let \({\mathcal B}(L)\), \({\mathcal G}(L)\) and \({\mathcal S}(L)\) denote the centre of \(L\), the automorphism group of \(L\) and the state space of \(L\). The author proves that given a Boolean algebra \(B\), a group \(G\) and a compact convex set \(S\), one can construct a quantum logic \(L(B,G,S)\) such that \({\mathcal B}(L(B,G,S))=B\), \({\mathcal G}(L(B,G,S))=G\) and \({\mathcal S}(L(B,G,S))=S\). Moreover, he shows that \(L(B,G,S)\) may be required to contain an arbitrary preassigned quantum logic. --- The proof technique is very interesting. The result itself is a highly valuable contribution to the theory of quantum logics and orthomodular structures.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 95563
zbMATH Keywords: logic embedding
zbMATH Keywords: centre
zbMATH Keywords: automorphism group
zbMATH Keywords: state space
zbMATH Keywords: compact convex set
zbMATH Keywords: orthomodular structures
author: Mirko Navara
reviewed by: Pavel Pták
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00675085
OpenAlex ID: W2049492630
description: scientific article; zbMATH DE number 95563