One-sided orthogonality, orthomodular spaces, quantum sets, and a class of Garside groups

DOI10.1016/j.jalgebra.2019.02.012zbMath1416.51004OpenAlexW2913785887WikidataQ128368478 ScholiaQ128368478MaRDI QIDQ1734217

Carsten Dietzel, Xia Zhang, Wolfgang Rump

Publication date: 22 March 2019

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2019.02.012

zbMATH Keywords

orthogonalitystructure groupGarside grouporthomodular spaceL-algebragroup valued measureright l-group

Mathematics Subject Classification ID

Noncommutative measure and integration (46L51) Combinatorial aspects of matroids and geometric lattices (05B35) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Congruence and orthogonality in metric geometry (51F20) Lattices of subspaces and geometric closure systems (51D25)

Related Items (8)

Commutative \(L\)-algebras and measure theory ⋮ Structure groups of \(L\)-algebras and Hurwitz action ⋮ The geometry of discrete \(L\)-algebras ⋮ Mini-workshop: Skew braces and the Yang-Baxter equation. Abstracts from the mini-workshop held February 26 -- March 4, 2023 ⋮ \(L\)-effect algebras ⋮ L-algebras with duality and the structure group of a set-theoretic solution to the Yang-Baxter equation ⋮ On the passage from finite braces to pre-Lie rings ⋮ Ortho-sets and Gelfand spectra

Cites Work

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• On the dynamics of (left) orderable groups.
• Von Neumann algebras, \(L\)-algebras, Baer*-monoids, and Garside groups
• On Frobenius algebras
• Right-ordered groups
• Braces, radical rings, and the quatum Yang-Baxter equation.
• \(L\)-algebras, self-similarity, and \(l\)-groups
• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Sheaves in geometry and logic: a first introduction to topos theory
• Groupes et anneaux reticules
• Orderings of mapping class groups after Thurston
• On the set-theoretical Yang-Baxter equation
• A characterization of finite multipermutation solutions of the Yang-Baxter equation
• The structure group of a generalized orthomodular lattice
• A right-invariant lattice-order on groups of paraunitary matrices
• The \(L\)-algebra of Hurwitz primes
• Orderable 3-manifold groups.
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Foundations of Garside theory
• Decomposition of Garside groups and self-similar \(L\)-algebras
• On L-spaces and left-orderable fundamental groups
• Finite quotients of groups of I-type.
• Parabolic subgroups of Garside groups.
• Right \(l\)-groups, geometric Garside groups, and solutions of the quantum Yang-Baxter equation
• Orthomodular lattices admitting no states
• Les immeubles des groupes de tresses généralises
• Artin-Gruppen und Coxeter-Gruppen
• On the geometry of projections in certain operator algebras
• Garside Groups and Yang–Baxter Equation
• Nielsen-Thurston orders and the space of braid orderings
• Groupes de Garside
• Ordered groups and topology
• Algebraic Analysis of Many Valued Logics
• SEMIDIRECT PRODUCTS IN ALGEBRAIC LOGIC AND SOLUTIONS OF THE QUANTUM YANG–BAXTER EQUATION
• Modular and Distributive Semilattices
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
• Pseudo MV-algebras are intervals in ℓ-groups
• Orthomodularity in infinite dimensions; a theorem of M. Solèr
• Left orders in Garside groups

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