On the possible temperatures of a dynamical system

DOI10.1007/BF01952891zbMath0437.46059OpenAlexW2087119424MaRDI QIDQ1141330

Richard H. Herman, George A. Elliott, Ola Bratteli

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1007/bf01952891

zbMATH Keywords

automorphism groupC*-dynamical systemK-theoryground statestemperaturesKMS-stateceiling statesConnes-Takesaki duality theoryinverse temperaturesK-theory for AF-algebrassimplex bundleunital AF-algebra

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) States of selfadjoint operator algebras (46L30) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Automorphisms of selfadjoint operator algebras (46L40)

Related Items

KMS states of quasi-free dynamics on Pimsner algebras, Locally semisimple algebras. Combinatorial theory and the \(K_ 0\)- functor, On the bundle of KMS state spaces for flows on a \(\mathcal{Z}\)-absorbing \(C^*\)-algebra, Crossed products of type I AF algebras by Abelian groups, Partition functions as \(C^*\)-dynamical invariants and actions of congruence monoids, Non-commutative shifts and crossed products., Equilibria when the temperature goes to zero, When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional?, PAIRS OF SIMPLE DIMENSION GROUPS, KMS states, conformal measures and ends in digraphs, Type III\(_{1}\) equilibrium states of the Toeplitz algebra of the affine semigroup over the natural numbers, \(C^\ast\)-crossed products by \(\mathbb R\). II, Introduction to M(atrix) theory and noncommutative geometry, The possible temperatures for flows on a simple AF algebra, Unbounded derivations in AT algebras, Generalized gauge actions on $\kappa$-graph $C*-Algebras: KMS states and Hausdorff structure, Period two automorphisms of UHF C*-algebras, Phase transition in the CAR algebra, Locally representable one-parameter automophism groups of AF algebras and KMS states, KMS spectra for group actions on compact spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the classification of the ordered groups associated with the approximately finite dimensional C*-algebras
• Some simple C*-algebras constructed as crossed products with discrete outer automorphism groups
• On a duality for crossed products of C\(^*\)-algebras
• Existence of ground states and KMS states for approximately inner dynamics
• On the classification of inductive limits of sequences of semisimple finite-dimensional algebras
• Trace states and KMS states for approximately inner dynamical one- parameter groups of \(^*\)-automorphisms
• Crossed products of UHF algebras by product type actions
• Appendix to O. Bratteli's paper on Crossed products of UHF algebras
• Simple \(C^*\)-algebras generated by isometries
• Dimension Groups and Their Affine Representations
• Unbounded Derivations of Group C ∗ -Algebras
• Some $C^*$-dynamical systems with a single KMS state.
• Poids et espérances conditionnelles dans les algèbres de von Neumann