Non-commutative methods for the K-theory of \(C^*\)-algebras of aperiodic patterns from cut-and-project systems

DOI10.1007/s00220-009-0968-0zbMath1213.46069OpenAlexW2011338160MaRDI QIDQ625469

Ian F. Putnam

Publication date: 17 February 2011

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-009-0968-0

zbMATH Keywords

K-theoryaperiodic structurescut-and-project methodhyperplane systemKK-groups

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) Dynamical aspects of cellular automata (37B15) Applications of functional analysis in quantum physics (46N50) Kasparov theory ((KK)-theory) (19K35)

Related Items

Long exact sequences of homology groups of étale groupoids ⋮ TWO-SIDED SHIFT SPACES OVER INFINITE ALPHABETS ⋮ Integral cohomology of rational projection method patterns ⋮ Ellis enveloping semigroup for almost canonical model sets of an Euclidean space ⋮ \(K\)-theory of crossed products of tiling \(C^*\)-algebras by rotation groups

Cites Work

• Continuity properties of the electronic spectrum of 1D quasicrystals
• On the \(K\)-theory of \(C^*\)-algebras of principal groupoids
• Topological invariants for projection method patterns
• On periodic and non-periodic space fillings ofE^mobtained by projection
• K-théorie des quasi-cristaux, image par la trace : le cas du réseau octogonal
• The cohomology and $K$-theory of commuting homeomorphisms of the Cantor set
• A spectral sequence for theK-theory of tiling spaces
• Quasiperiodic patterns and icosahedral symmetry
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