The Heisenberg group and \(K\)-theory

DOI10.1007/BF00961535zbMath0803.46076OpenAlexW2045522200MaRDI QIDQ1317439

Ryszard Nest, Toshikazu Natsume, George A. Elliott

Publication date: 2 January 1995

Published in: \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00961535

zbMATH Keywords

\(C^*\)-dynamical systemBott periodicitycontinuous fields of \(C^*\)-algebrasAtiyah-Singer theoremcanonical isomorphism of Abelian groupsConnes isomorphism theorem

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55)

Related Items

The Atiyah-Singer index theorem as passage to the classical limit in quantum mechanics, Operations on continuous bundles of \(C^*\)-algebras, Kepplers Phoronomie: Symplektische Spinoren. (Keppler's phoronomy: Symplectic spinors), On stably finiteness for \(C^*\)-algebras of exponential solvable Lie groups, The Connes-Kasparov conjecture for almost connected groups and for liner \(p\)-adic groups, Déformations de $C\sp*$-algèbres de Hopf, Approximate ideal structures and \(K\)-theory, A cohomological formula for the Atiyah–Patodi–Singer index on manifolds with boundary, Boundary maps for \(C^*\)-crossed products with \(\mathbb R\) with an application to the quantum Hall effect, An invariant for unbounded operators, Diagonalizing operators in Hilbert modules over \(C^*\)-algebras, An introduction to 3D discrete magnetic Laplacians and noncommutative 3-tori, Gap labelling and the pressure on the boundary

Cites Work

• Non-commutative differential geometry
• Continuous fields of \(C^*\)-algebras coming from group cocycles and actions
• Cyclic cohomology for one-parameter smooth crossed products
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• Connes' analogue of the Thom Isomorphism for the Kasparov groups
• On a duality for crossed products of C\(^*\)-algebras
• On representations of discrete, finitely generated, torsion-free, nilpotent groups
• The Atiyah-Singer index theorem as passage to the classical limit in quantum mechanics
• The stable homotopy of the classical groups
• Produits croises d'une \(C^ *\)-algèbre par un groupe d'automorphismes
• Topological representation of \(C^ *\)-algebras
• A Simple Proof of the Dauns-Hofmann Theorem.
• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
• Sur Les Representations Unitaires des Groupes de Lie Nilpotents. VI
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item