Active lattices determine \(\mathrm{AW}^\ast\)-algebras

DOI10.1016/j.jmaa.2014.02.041zbMath1310.46053arXiv1212.5778OpenAlexW2087550382MaRDI QIDQ402977

Chris Heunen, Manuel L. Reyes

Publication date: 29 August 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5778

zbMATH Keywords

symmetryprojectioncategory\(\mathrm{AW}^\ast\)-algebraactive latticepiecewise complete Boolean algebraunitary action

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Abstract operator algebras on Hilbert spaces (47L30)

Related Items (18)

Symmetries of C ∗-algebras and Jordan Morphisms ⋮ \(L\)-algebras and three main non-classical logics ⋮ A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors ⋮ Characterizations of categories of commutative \(C^*\)-subalgebras ⋮ Tarski monoids: Matui's spatial realization theorem ⋮ The finite dual coalgebra as a quantization of the maximal spectrum ⋮ The paraunitary group of a von Neumann algebra ⋮ On the structure of closed right ideals of a \(C^*\)-algebra ⋮ Classifying finite-dimensional \(C^*\)-algebras by posets of their commutative \(C^*\)-subalgebras ⋮ Maps preserving products of commuting elements in von Neumann algebras ⋮ Unnamed Item ⋮ Contextuality and noncommutative geometry in quantum mechanics ⋮ Dye's theorem and Gleason's theorem for \(AW^\ast\)-algebras ⋮ Automorphisms of order structures of abelian parts of operator algebras and their role in quantum theory ⋮ Piecewise \(^\ast\)-homomorphisms and Jordan maps on \(C^\ast\)-algebras and factor von Neumann algebras ⋮ Boolean subalgebras of orthoalgebras ⋮ Additivity of quadratic maps on JB algebras ⋮ Domains of commutative C*-subalgebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Characterizations of categories of commutative \(C^*\)-subalgebras
• Noncommutativity as a colimit
• Equivalence and perspectivity in Baer rings
• Stone duality and Gleason covers through de Vries duality
• A factor not anti-isomorphic to itself
• On Dye's theorem for Jordan operator algebras
• Obstructing extensions of the functor Spec to noncommutative rings
• Diagonalizing matrices over \(AW^\ast\)-algebras
• Isomorphisms of ordered structures of Abelian \(C^*\)-subalgebras of \(C^*\)-algebras
• Commutateurs dans le groupe unitaire d'un facteur
• The commutator and solvability in a generalized orthomodular lattice
• Projections in Banach algebras
• On the geometry of projections in certain operator algebras
• THE GELFAND SPECTRUM OF A NONCOMMUTATIVE C*-ALGEBRA: A TOPOS-THEORETIC APPROACH
• Orthosymmetric Ortholattices
• The Mackey-Gleason Problem
• A Unitary as a Product of Symmetries
• No-go theorems for functorial localic spectra of noncommutative rings
• On the Jordan Structure of C ∗ -Algebras
• On Matrices Over the Ring of Continuous Complex Valued Functions on a Stonian Space
• An m-Orthocomplete Orthomodular Lattice is m-Complete
• Baer ∗ -Semigroups
• Infinite Unitary Groups
• Theory of operator algebras I.

This page was built for publication: Active lattices determine \(\mathrm{AW}^\ast\)-algebras