46L55 — 6 articles found.
Actions of $({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})$ on Lattice Ordered Dimension Groups
Andrew J. Dean, Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada P7B 5E1; e-mail: ajdean@lakeheadu.ca
Sarah K. Lucky , Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada P7B 5E1; e-mail: sklucky@lakeheadu.ca
Abstract/Résumé:
It is shown that if \(G\) is a lattice ordered countable group, then every action of \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) on \(G\) arises as an inductive limit of actions of \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) on simplicial groups. Some parts of the argument work in greater generality, and are proved for general finite abelian groups. A template is given for proving similar results for other such groups.
On montre que si \(G\) est un groupe dénombrable treillis-ordonné, alors toute action de \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) sur \(G\) provient d’une limite inductive d’actions de \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) sur des groupes simpliciaux. Des parties de cet argument fonctionnent dans une généralité plus grande et sont prouvées pour des groupes abéliens finis en général. Un modèle est donné pour prouver des résultats similaires pour d’autres groupes de ce type.
Keywords: Dimension groups, K-theory, classification
AMS Subject Classification:
Classifications of $C^*$-algebras; factors, Noncommutative dynamical systems
46L35, 46L55
PDF(click to download): Actions of $({Z}/2{Z})$ x $({Z}/2{Z})$ on Lattice Ordered Dimension Groups
The Bundle of KMS State Spaces for Flows on a Unital AF C*-algebra
George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4; e-mail: elliott@math.toronto.edu
Klaus Thomsen, Department of Mathematics, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark; e-mail: matkt@math.au.dk
Abstract/Résumé:
It is shown that, for any unital simple infinite-dimensional AF algebra, the KMS-state bundle for a one-parameter automorphism group is isomorphic to an arbitrary proper simplex bundle over the real line with (as is necessary) fibre at (inverse temperature) zero isomorphic to the trace simplex.
On démontre que, pour toute C*-algèbre AF simple à élément unité et à dimension infinie, le faisceau d’états KMS pour un grouped’automorphismes à un paramètre est isomorphe à un faisceau de simplices propre arbitraire sur la ligne réelle tel que (nécessairement) le fibre sur la température inverse zéro est isomorphe au simplex tracial.
Keywords: One-parameter automorphism group of an AF algebra, bundle of equilibrium (KMS) states arbitrary
AMS Subject Classification:
General theory of $C^*$-algebras, Noncommutative dynamical systems
46L05, 46L55
PDF(click to download): The Bundle of KMS State Spaces for Flows on a Unital AF C*-algebra
KMS States for the Generalized Gauge Action on Graph Algebras
Gilles G. de Castro, Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-970 Florianópolis SC, Brazil; e-mail: gilles.castro@ufsc.br
Fernando de L. Mortari, Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-970 Florianópolis SC, Brazil; e-mail: fernando.mortari@ufsc.br
Abstract/Résumé:
Given a positive function on the set of edges of an arbitrary directed graph \(E=(E^0,E^1)\), we define a one-parameter group of automorphisms on the C*-algebra of the graph \(C^*(E)\), and study the problem of finding KMS states for this action. We prove that there are bijective correspondences between KMS states on \(C^*(E)\), a certain class of states on its core, and a certain class of tracial states on \(C_0(E^0)\). We also find the ground states for this action and give some examples.
Étant donné une fonction positive sur l’ensemble des arcs d’un graphe orienté arbitraire \(E=(E^0,E^1)\), nous définissons un groupe à un paramètre d’automorphismes de la \(C^*\)-algèbre du graphe \(C^*(E)\), et nous étudions le problème de trouver les états KMS pour cette action. Nous prouvons qu’il existe des bijections entre les états KMS sur \(C^*(E)\), une certaine classe d’états sur le core, et une certaine classe détats traciaux sur \(C_0(E^0)\). Nous trouvons également les états fondamentaux pour cette action et nous donnons quelques exemples.
Keywords: C*-algebra, Graph, Ground state, KMS state
AMS Subject Classification:
Noncommutative dynamical systems
46L55
PDF(click to download): KMS States for the Generalized Gauge Action on Graph Algebras
The ordered K0-group of a graph C*-algebra
M. Tomforde
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords:
AMS Subject Classification:
Noncommutative dynamical systems
46L55
PDF(click to download): The ordered K0-group of a graph C*-algebra
Maximal abelian subalgebras of?n
E.J. Beggs / P. Goldstein
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords:
AMS Subject Classification:
Tensor products of $C^*$-algebras, Classifications of $C^*$-algebras; factors, Noncommutative dynamical systems
46L06, 46L35, 46L55
PDF(click to download): Maximal abelian subalgebras of ?n
Index theory and quantization of boundary value problems
P.E.T. Jorgensen / G.L. Price
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords:
AMS Subject Classification:
Automorphisms, Noncommutative dynamical systems,
46L40, 46L55, 47D45
PDF(click to download): Index theory and quantization of boundary value problems