The structure group of a generalized orthomodular lattice
type: Item
instance of: scholarly article
title: The structure group of a generalized orthomodular lattice
zbMATH Open document ID: 1412.06011
author: Wolfgang Rump
published in: Studia Logica
publication date: 2018-04-04T00:00:00Z
review text: The author uses a dual definition of a generalized orthomodular lattice using axioms for the (upper) orthogonality relation and assuming the existence of a greatest element but not the existence of a least element. He characterizes generalized orthomodular lattices as singular \(L\)-algebras, shows that generalized orthomodular lattices correspond to orthomodular lattices with two-valued Jauch-Piron state. The main result states that there is a one-to-one correspondence between generalized orthomodular lattices and right \(\ell\)-groups of singular type (the correspondence is explicitly described).
reviewed by: Josef Tkadlec
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 06F15
zbMATH DE Number: 6855868
zbMATH Keywords: generalized orthomodular lattice
zbMATH Keywords: L-algebra
zbMATH Keywords: right \(\ell\)-group
zbMATH Keywords: Garside group
zbMATH Keywords: Jauch-Piron state
zbMATH Keywords: group-valued measure
MaRDI profile type: Publication
full work available at URL: s11225-017-9726-z
OpenAlex ID: W2612460719
cites work: Theory of braids
cites work: Groupes et anneaux reticules
cites work: The logic of quantum mechanics
cites work: Rechtskomplementäre Halbgruppen, Axiome, Polynome, Kongruenzen
cites work: Orderable 3-manifold groups.
cites work: Artin-Gruppen und Coxeter-Gruppen
cites work: Garside Groups and Yang–Baxter Equation
cites work: Finite quotients of groups of I-type.
cites work: Right-ordered groups
cites work: Q4317872
cites work: Groupes de Garside
cites work: Foundations of Garside theory
cites work: Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
cites work: Les immeubles des groupes de tresses généralises
cites work: Set-theoretical solutions to the quantum Yang-Baxter equation
cites work: Conditions for the modularity of an orthomodular lattice
cites work: Implication connectives in orthomodular lattices
cites work: Q5555716
cites work: Q5551052
cites work: The lattice theoretic background of the dimension theory of operator algebras
cites work: Q5638775
cites work: Q3669960
cites work: An Orthomodular Lattice Admitting No Group-Valued Measure
cites work: On the dynamics of (left) orderable groups.
cites work: Nielsen-Thurston orders and the space of braid orderings
cites work: The center of thin Gaussian groups
cites work: Q5516132
cites work: Jauch–Piron states
cites work: A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
cites work: \(L\)-algebras, self-similarity, and \(l\)-groups
cites work: SEMIDIRECT PRODUCTS IN ALGEBRAIC LOGIC AND SOLUTIONS OF THE QUANTUM YANG–BAXTER EQUATION
cites work: Right \(l\)-groups, geometric Garside groups, and solutions of the quantum Yang-Baxter equation
cites work: Decomposition of Garside groups and self-similar \(L\)-algebras
cites work: Von Neumann algebras, \(L\)-algebras, Baer*-monoids, and Garside groups
cites work: Q5826968
cites work: Orderings of mapping class groups after Thurston
DOI: 10.1007/S11225-017-9726-Z
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description: scientific article; zbMATH DE number 6855868