Symmetries and retracts of quantum logics
type: Item
instance of: scholarly article
title: Symmetries and retracts of quantum logics
zbMATH Open document ID: 0626.06013
DOI: 10.1007/BF00672386
author: Jianyong Qiao
author: Sumit K. Garg
published in: International Journal of Theoretical Physics
publication date: 1987-01-01T00:00:00Z
review text: The authors call a pair \(Q=(L,M)\) a quantum logic if L is an orthomodular \(\sigma\)-lattice and M is a \(\sigma\)-convex full set of states on L. A symmetry of Q is an automorphism \(\tau\) of L with \(\{\) \(m\circ \tau |\) \(m\in M\}=M\). Let \(\{G_ i|\) \(i\in I\}\) be a family of groups, \(\leq\) a partial order on I and Q a fixed quantum logic. It is shown that there exists a family \(\{Q_ i|\) \(i\in I\}\) of quantum logics such that Q is a sublogic of every \(Q_ i\), \(Q_ i\) has \(G_ i\) as group of symmetries and \(Q_ i\) is a retract of \(Q_ j\) for \(i\leq j\). For \(i\nleq j\), \(Q_ i\) is not a sublogic of \(Q_ j\). This result strengthens the result of \textit{G. Kalmbach} [Bull. Aust. Math. Soc. 29, 309-313 (1984; Zbl 0538.06009)].
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 4016973
zbMATH Keywords: orthomodular \(\sigma \)-lattice
zbMATH Keywords: states
zbMATH Keywords: automorphism
zbMATH Keywords: quantum logics
zbMATH Keywords: group of symmetries
Wikidata QID: Q114672381
reviewed by: Gudrun Kalmbach
MaRDI profile type: Publication
cites work: Q4750696
cites work: Automorphism groups of orthomodular lattices
cites work: Q5723020
cites work: Symmetries in quantum logics
cites work: Q3208855
cites work: Graphs with Given Group and Given Graph-Theoretical Properties
full work available at URL: https://doi.org/10.1007/bf00672386
OpenAlex ID: W2071291446
description: scientific article; zbMATH DE number 4016973