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46L55, Noncommutative dynamical systems — 5 results found.

      
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The Bundle of KMS State Spaces for Flows on a Unital AF C*-algebra
C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (4) 2021, pp. 103-121
George A. Elliott; Klaus Thomsen (Received: 2021/09/21)

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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.

KMS States for the Generalized Gauge Action on Graph Algebras
C. R. Math. Rep. Acad. Sci. Canada Vol. 36 (4) 2014, pp. 114–128
Gilles G. de Castro; Fernando de L. Mortari (Received: 2014/05/17, Revised: 2014/07/10)

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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.

The ordered K0-group of a graph C*-algebra
C. R. Math. Rep. Acad. Sci. Canada Vol. 25 (1) 2003, pp. 19–25
M. Tomforde (Received: 2002/10/20)

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Maximal abelian subalgebras of?n
C. R. Math. Rep. Acad. Sci. Canada Vol. 24 (1) 2002, pp. 26–32
E.J. Beggs / P. Goldstein (Received: 2001/05/11)

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Index theory and quantization of boundary value problems
C. R. Math. Rep. Acad. Sci. Canada Vol. 11 (6) 1989, pp. 237–242
P.E.T. Jorgensen / G.L. Price (Received: 1989/09/08)

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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