Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
Abstract
We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This extends Cuntz's classical decomposition for Cuntz algebras and reveals an implicit symmetric structure within these algebras. Exploiting this structure, we characterize their simplicity and classify their ideals, tracial weights, and KMS weights for generalized quasi-free flows, revisiting and refining seminal results by Kitamura, Schweizer, and Laca--Neshveyev. We also give a short, elementary solution to the reduced Hao--Ng isomorphism problem for locally compact groups in full generality. Bypassing non-self-adjoint operator algebra techniques used in prior work, our proof relies solely on C*-algebra theory. In contrast, we disprove the full Hao--Ng conjecture by constructing counterexamples. Combining these results, we investigate quasi-free actions on Cuntz algebras. Notably, we affirmatively answer a recent question posed by Izumi on isometric shift-absorption for compact groups.
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BibTeX
@misc{mukohara2026stabilization,
title = {{Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras}},
author = {Miho Mukohara and Yuhei Suzuki},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.21128},
eprint = {2605.21128},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21128},
}
RIS
TY - UNPB
TI - Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
AU - Miho Mukohara
AU - Yuhei Suzuki
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2605.21128
UR - https://arxiv.org/abs/2605.21128
AB - We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This extends Cuntz's classical decomposition for Cuntz algebras and reveals an implicit symmetric structure within these algebras. Exploiting this structure, we characterize their simplicity and classify their ideals, tracial weights, and KMS weights for generalized quasi-free flows, revisiting and refining seminal results by Kitamura, Schweizer, and Laca--Neshveyev. We also give a short, elementary solution to the reduced Hao--Ng isomorphism problem for locally compact groups in full generality. Bypassing non-self-adjoint operator algebra techniques used in prior work, our proof relies solely on C*-algebra theory. In contrast, we disprove the full Hao--Ng conjecture by constructing counterexamples. Combining these results, we investigate quasi-free actions on Cuntz algebras. Notably, we affirmatively answer a recent question posed by Izumi on isometric shift-absorption for compact groups.
ER -