Simple Bratteli diagrams with a Gödel-incomplete C*-equivalence problem

DOI10.1090/S0002-9947-03-03353-1zbMath1042.46033MaRDI QIDQ4452268

Daniele Mundici

Publication date: 12 February 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

\(C^*\)-equivalenceDe Concini-Procesi theorem for toric varietiesElliott's classificationisomorphism of Bratteli diagramsMarkov undecidability theoremstable AF-algebra

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Classifications of (C^*)-algebras (46L35) Word problems, etc. in computability and recursion theory (03D40) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (12)

The Lebesgue state of a unital abelian lattice-ordered group ⋮ Recognizing free generating sets of \(\ell\)-groups ⋮ Revisiting the free 2-generator abelian \(\ell\)-group ⋮ Word problems in Elliott monoids ⋮ Fans, decision problems and generators of free abelian \(\ell\)-groups ⋮ Symbolic substitutions, Bratteli diagrams and operator algebras ⋮ Gödel incompleteness in AF C*-algebras ⋮ Bratteli diagrams via the De Concini–Procesi theorem ⋮ Set Theory and C*-Algebras ⋮ Free generating sets of lattice-ordered abelian groups ⋮ Recognizing the Farey-Stern-Brocot AF algebra ⋮ Lattice-ordered Abelian groups and Schauder bases of unimodular fans

Cites Work

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• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Satisfiability in many-valued sentential logic is NP-complete
• Farey stellar subdivisions, ultrasimplicial groups, and \(K_ 0\) of AF \(C^*\)-algebras
• Groupes et anneaux reticules
• Classes of ultrasimplicial lattice-ordered abelian groups
• A characterisation of lattice-ordered Abelian groups
• Every Abelian \(\ell\)-group is ultrasimplicial
• The Word Problem Versus the Isomorphism Problem
• Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
• Non-stationarity of isomorphism between AF algebras defined by stationary Bratteli diagrams
• Inductive Limits of Finite Dimensional C ∗ -Algebras

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