KMS and ground states for the normalized dynamics of the tame C*-algebras 𝒪m,n
Abstract
We study KMS and ground states of the tame C*-algebras 𝒪m,n of Ara, Exel and Katsura under the dynamics σt(si)=mitsi, σt(tj)=nittj. Normalized restriction to the full corner A=q𝒪m,nq, generated by the partial isometries vij=si*tj of common energy log(n/m), is at each inverse temperature β an affine weak-* homeomorphism of the two systems. Let m,n≥ 2. When m=n the corner dynamics is trivial, so the KMS simplices are identified with trace simplices. When m≠ n, KMS states occur only at β=1, and there they are not unique. Conformal branching models surject the KMS1 simplex onto a transportation polytope of dimension $(m-1)(n-1)$, whose vertices lift to extremal, hence factorial, KMS1 states, the fibre over each vertex being itself the KMS1 simplex of a quotient of A.
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BibTeX
@misc{pinto2026ground,
title = {{KMS and ground states for the normalized dynamics of the tame $C^*$-algebras $\mathcalO_m,n$}},
author = {Paulo R. Pinto and Filipe Viseu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30544},
eprint = {2609.30544},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30544},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - KMS and ground states for the normalized dynamics of the tame C^*-algebras 𝒪_m,n
AU - Paulo R. Pinto
AU - Filipe Viseu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30544
UR - https://arxiv.org/abs/2609.30544
AB - We study KMS and ground states of the tame C^*-algebras 𝒪_m,n of Ara, Exel and Katsura under the dynamics σ_t(s_i)=m^its_i, σ_t(t_j)=n^itt_j. Normalized restriction to the full corner A=q𝒪_m,nq, generated by the partial isometries v_ij=s_i^*t_j of common energy log(n/m), is at each inverse temperature β an affine weak-* homeomorphism of the two systems. Let m,n≥ 2. When m=n the corner dynamics is trivial, so the KMS simplices are identified with trace simplices. When m≠ n, KMS states occur only at β=1, and there they are not unique. Conformal branching models surject the KMS_1 simplex onto a transportation polytope of dimension $(m-1)(n-1)$, whose vertices lift to extremal, hence factorial, KMS_1 states, the fibre over each vertex being itself the KMS_1 simplex of a quotient of A.
ER -