Locally semisimple algebras. Combinatorial theory and the \(K_ 0\)- functor

DOI10.1007/BF01088200zbMath0623.46036OpenAlexW2073215417MaRDI QIDQ1091576

Sergei Kerov, Anatoly M. Vershik

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01088200

zbMATH Keywords

classificationgroup algebrasMarkov chainsprojective modulesbifurcation graphmultiplicity functionlocally semisimpleRiesz groupsAF- algebrasapproximately dynamical systemsBratteli's diagrammChoquet simplex of central measuresGrothendieck K(sub O)-groupsHandelman-Effros-Shen's axiomatic description of ordered groups isomorphic to the Grothendieck groups of LS-algebrasideals and traces of AF-algebrasindecomposable cohomology cocycleinductive systemsK-theory of locally semisimple algebrasLS-algebrasquasi-invariant ergodic measure

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Classifications of (C^*)-algebras (46L35)

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Cites Work

• The K-functor (Grothendieck group) of the infinite symmetric group
• Asymptotics of maximal and typical dimensions of irreducible representations of a symmetric group
• On dimension functions and topological Markov chains
• A groupoid approach to C*-algebras
• On the possible temperatures of a dynamical system
• The geometry of finite rank dimension groups
• Automorphisms of dimension groups and the construction of AF algebras
• The center of approximately finite-dimensional \(C^*\)-algebras
• Rank functions and \(K_0\) of regular rings
• On the classification of inductive limits of sequences of semisimple finite-dimensional algebras
• Algebraic representations of Choquet simplexes
• Structure spaces of approximately finite-dimensional C*-algebras. II
• Structure spaces of approximately finite-dimensional C\(^*\)-algebras
• A theorem on the Markov periodic approximation in ergodic theory
• On some \(C^ *\)-algebras considered by Glimm
• Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
• The Representation of Partition Structures
• Extensions for AF C ∗ Algebras and Dimension Groups
• The Characters of the Infinite Symmetric Group and Probability Properties of the Robinson–Schensted–Knuth Algorithm
• Affine representations of Grothendieck groups and applications to Rickart 𝐶*-algebras and ℵ₀-continuous regular rings
• Approximately Finite Dimensional C ∗ -Algebras and Bratteli Diagrams
• Dimension Groups and Their Affine Representations
• The Spectral Theory of Posets and Its Applications to C ∗ -Algebras
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• A Simple C ∗ -Algebra with no Nontrivial Projections
• K₀ OF VON NEUMANN AND AF C^* ALGEBRAS
• METRIC COMPLETIONS OF DIMENSION GROUPS AND THE GELFAND-NAIMARK-SEGAL CONSTRUCTION
• Inductive Limits of Finite Dimensional C ∗ -Algebras
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