arXiv subjects

Miho Mukohara

Publications and source records attributed to Miho Mukohara.

4 recordsLinked to original sources

arXiv2026

Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras

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.

math.OA↗

arXiv2026

Properly Outer Actions of Tensor Categories on C$^*$-algebras

We discuss proper outerness for finite index endomorphisms and finite index bimodules of simple C$^*$-algebras, extending recent similar results by Izumi concerning the purely infinite setting. Our main result is that proper outerness holds automatically for finite index outer endomorphisms of simple C$^*$-algebras. Consequently, freeness for outer actions of unitary tensor categories on simple C$^*$-algebras is also shown to hold automatically. As applications, we obtain structural results about potentially infinite index irreducible discrete inclusions of C$^*$-algebras, such as C$^*$-irreducibility.

math.OA↗

arXiv2024

Inclusions of simple C$^*$-algebras arising from compact group actions

Inclusions of operator algebras have long been studied. In particular, inclusions arising from actions of compact groups on factors were studied by Izumi-Longo-Popa and others. The correspondence between intermediate subfactors and subgroups is called the Galois correspondence. Analogues for actions on C$^*$-algebras have been studied by Izumi, Cameron-Smith, Peligrad, and others. In this article, we show the Galois correspondence for quasi-product actions of compact groups on C*-algebras. The notion of a quasi-product action was introduced by Bratteli-Elliott-Kishimoto. Recently, Izumi proved that every minimal action with a simple fixed-point algebra is a quasi-product action. According to these results, we get the Galois correspondence for minimal actions of compact groups with separable simple fixed point algebras. In addition, this paper provides another proof of the Galois correspondence for isometrically shift-absorbing actions and free product actions.

math.OA↗

arXiv2022

C*-simplicity of relative profinite completions of generalized Baumslag-Solitar groups

Suzuki recently gave constructions of non-discrete examples of locally compact C*-simple groups and Raum showed C*-simplicity of the relative profinite completions of the Baumslag-Solitar groups by using Suzuki's results. We extend this result to some fundamental groups of graphs of groups called generalized Baumslag-Solitar groups. In this article, we focus on some sufficient condition to show that these locally compact groups are C*-simple and that KMS-weights of these reduced group C*-algebras are unique. This condition is an analogue of the Powers averaging property of discrete groups and holds for several currently known constructions of non-discrete C*-simple groups.

math.OA↗