Abstract
We study Kubo-Martin-Schwinger (KMS) states on finite-graph C*-algebras with sinks and sources. We compare finite-graph C*-algebras with C*-algebras associated with complex dynamical systems of rational functions. We show that if the inverse temperature β is large, then the set of extreme β-KMS states is parametrized by the set of sinks of the graph. This means that the sinks of a graph correspond to the branched points of a rational function from the point of KMS states. Since we consider graphs with sinks and sources, left actions of the associated bimodules are not injective. Then the associated graph C*-algebras are realized as (relative) Cuntz-Pimsner algebras studied by Katsura. We need to generalize Laca-Neshvyev's theorem of the construction of KMS states on Cuntz-Pimsner algebras to the case that left actions of bimodules are not injective.
| Original language | English |
|---|---|
| Pages (from-to) | 83-104 |
| Number of pages | 22 |
| Journal | Kyushu Journal of Mathematics |
| Volume | 67 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jul 25 2013 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
KMS states on finite-graph C*-algebras. / Kajiwara, Tsuyoshi; Watatani, Yasuo.
In: Kyushu Journal of Mathematics, Vol. 67, No. 1, 25.07.2013, p. 83-104.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - KMS states on finite-graph C*-algebras
AU - Kajiwara, Tsuyoshi
AU - Watatani, Yasuo
PY - 2013/7/25
Y1 - 2013/7/25
N2 - We study Kubo-Martin-Schwinger (KMS) states on finite-graph C*-algebras with sinks and sources. We compare finite-graph C*-algebras with C*-algebras associated with complex dynamical systems of rational functions. We show that if the inverse temperature β is large, then the set of extreme β-KMS states is parametrized by the set of sinks of the graph. This means that the sinks of a graph correspond to the branched points of a rational function from the point of KMS states. Since we consider graphs with sinks and sources, left actions of the associated bimodules are not injective. Then the associated graph C*-algebras are realized as (relative) Cuntz-Pimsner algebras studied by Katsura. We need to generalize Laca-Neshvyev's theorem of the construction of KMS states on Cuntz-Pimsner algebras to the case that left actions of bimodules are not injective.
AB - We study Kubo-Martin-Schwinger (KMS) states on finite-graph C*-algebras with sinks and sources. We compare finite-graph C*-algebras with C*-algebras associated with complex dynamical systems of rational functions. We show that if the inverse temperature β is large, then the set of extreme β-KMS states is parametrized by the set of sinks of the graph. This means that the sinks of a graph correspond to the branched points of a rational function from the point of KMS states. Since we consider graphs with sinks and sources, left actions of the associated bimodules are not injective. Then the associated graph C*-algebras are realized as (relative) Cuntz-Pimsner algebras studied by Katsura. We need to generalize Laca-Neshvyev's theorem of the construction of KMS states on Cuntz-Pimsner algebras to the case that left actions of bimodules are not injective.
UR - http://www.scopus.com/inward/record.url?scp=84880768062&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84880768062&partnerID=8YFLogxK
U2 - 10.2206/kyushujm.67.83
DO - 10.2206/kyushujm.67.83
M3 - Article
AN - SCOPUS:84880768062
VL - 67
SP - 83
EP - 104
JO - Kyushu Journal of Mathematics
JF - Kyushu Journal of Mathematics
SN - 1340-6116
IS - 1
ER -