Partial Dynamical Systems and the KMS Condition |
| |
Authors: | Ruy Exel Marcelo Laca |
| |
Institution: | (1) Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis SC, Brazil, BR;(2) Department of Mathematics, University of Newcastle, NSW 2308, Australia., AU |
| |
Abstract: | Given a countably infinite 0–1 matrix A without identically zero rows, let 𝒪
A
be the Cuntz–Krieger algebra recently introduced by the authors and 𝒯
A
be the Toeplitz extension of 𝒪
A
, once the latter is seen as a Cuntz–Pimsner algebra, as recently shown by Szymański. We study the KMS equilibrium states
of C
*
-dynamical systems based on 𝒪
A
and 𝒯
A
, with dynamics satisfying for the canonical generating partial isometries s
x
and arbitrary real numbers N
x
> 1. The KMSβ states on both 𝒪
A
and 𝒯
A
are completely characterized for certain values of the inverse temperature β, according to the position of β relative to
three critical values, defined to be the abscissa of convergence of certain Dirichlet series associated to A and the N(x). Our results for 𝒪
A
are derived from those for 𝒯
A
by virtue of the former being a covariant quotient of the latter. When the matrix A is finite, these results give theorems of Olesen and Pedersen for 𝒪
n
and of Enomoto, Fujii and Watatani for 𝒪
A
as particular cases.
Received: 21 November 2000 / Accepted: 31 May 2002 Published online: 22 November 2002
RID="*"
ID="*" Partially supported by CNPq
RID="**, ***" |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|