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Yuhei Suzuki

Publications and source records attributed to Yuhei Suzuki.

At least 19 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.

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arXiv2024

Crossed product splitting of intermediate operator algebras via 2-cocycles

We investigate the C*-algebra inclusions $B \subset A \rtimes_{\rm r} \Gamma$ arising from inclusions $B \subset A$ of $\Gamma$-C*-algebras. The main result shows that, when $B \subset A$ is C*-irreducible in the sense of R{\o}rdam, and is centrally $\Gamma$-free in the sense of the author, then after tensoring with the Cuntz algebra $\mathcal{O}_2$, all intermediate C*-algebras $B \subset C\subset A \rtimes_{\rm r} \Gamma$ enjoy a natural crossed product splitting \[\mathcal{O}_2\otimes C=(\mathcal{O}_2 \otimes D) \rtimes_{{\rm r}, \gamma, \mathfrak{w}} \Lambda\] for $D:= C \cap A$, some $\Lambda<\Gamma$, and a subsystem $(\gamma, \mathfrak{w})$ of a unitary perturbed cocycle action $\Lambda \curvearrowright \mathcal{O}_2\otimes A$. As an application, we give a new Galois's type theorem for the Bisch--Haagerup type inclusions \[A^K \subset A\rtimes_{\rm r} \Gamma\] for actions of compact-by-discrete groups $K \rtimes \Gamma$ on simple C*-algebras. Due to a K-theoretical obstruction, the operation $\mathcal{O}_2\otimes -$ is necessary to obtain the clean splitting. Also, in general 2-cocycles $\mathfrak{w}$ appearing in the splitting cannot be removed even further tensoring with any unital (cocycle) action. We show them by examples, which further show that $\mathcal{O}_2$ is a minimal possible choice. We also establish a von Neumann algebra analogue, where $\mathcal{O}_2$ is replaced by the type I factor $\mathbb{B}(\ell^2(\mathbb{N}))$.

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arXiv2024

Amenable actions on ill-behaved simple C*-algebras

By combining R{\o}rdam's construction and the author's previous construction, we provide the first examples of amenable actions of non-amenable groups on simple separable nuclear C*-algebras that are neither stably finite nor purely infinite. For free groups, we also provide unital examples. We arrange the actions so that the crossed products are still simple with both a finite and an infinite projection.

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arXiv2024

Simplicity and tracial weights on non-unital reduced crossed products

We extend theorems of Breuillard-Kalantar-Kennedy-Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of C*-algebras is stable under taking reduced crossed product over discrete C*-simple groups, and a similar result for uniqueness of tracial weight. Interestingly, our analysis on tracial weights involves von Neumann algebra theory. Our generalizations have two applications. The first is to locally compact groups. We establish stability results of (non-discrete) C*-simplicity and the unique trace property under discrete group extensions. The second is to the twisted crossed product. Thanks to the Packer-Raeburn theorem, our results lead to (generalizations of) the results of Bryder-Kennedy by a different method.

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arXiv2023

Amenable actions on finite simple C*-algebras arising from flows on Pimsner algebras

Associated to a family of $G$-$\ast$-endomorphisms on a $G$-C*-algebra $A$ satisfying certain minimality conditions, we give a $G$-C*-correspondence $\mathcal{E}$ over $A$ whose Cuntz--Pimsner algebra $\mathcal{O}_\mathcal{E}$ is simple. For certain quasi-free flows $γ$ (commuting with the $G$-action) on $\mathcal{O}_\mathcal{E}$, we further prove the simplicity of the reduced crossed product $\mathcal{O}_\mathcal{E} \rtimes_γ\mathbb{R}$. We then classify the KMS weights of $γ$. This in particular gives a sufficient condition for $\mathcal{O}_\mathcal{E}$ and $\mathcal{O}_\mathcal{E}\rtimes_γ\mathbb{R}$ to be stably finite (and to be stably projectionless). As the amenability of $G \curvearrowright A$ inherits to the induced actions $G \curvearrowright \mathcal{O}_\mathcal{E}, \mathcal{O}_\mathcal{E}\rtimes_γ\mathbb{R}$, this provides a new systematic framework to provide amenable actions on stably finite simple C*-algebras.

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arXiv2023

Photochemical and RadiatiOn Transport model for Extensive USe (PROTEUS)

We introduce a new flexible one-dimensional photochemical model named Photochemical and RadiatiOn Transport model for Extensive USe (PROTEUS), which consists of a Python graphical user interface (GUI) program and Fortran 90 modules. PROTEUS is designed for adaptability to many planetary atmospheres, for flexibility to deal with thousands of or more chemical reactions with high efficiency, and for intuitive operation with GUI. Chemical reactions can be easily implemented into the Python GUI program in a simple string format, and users can intuitively select a planet and chemical reactions on GUI. Chemical reactions selected on GUI are automatically analyzed by string parsing functions in the Python GUI program, then applied to the Fortran 90 modules to simulate with the selected chemical reactions on a selected planet. PROTEUS can significantly save the time for those who need to develop a new photochemical model; users just need to write chemical reactions in the Python GUI program and just select them on GUI to run a new photochemical model.

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arXiv2022

C*-simplicity has no local obstruction

In 2016, I solved a problem of de la Harpe in 2006: Is there a non-discrete C*-simple group? However the solution was not fully satisfactory as the provided C*-simple groups (and their operator algebras) are very close to discrete groups. All previously known examples are of this form. In this article I give yet another construction of non-discrete C*-simple groups. The statement in the title then follows. This in particular gives the first examples of non-elementary C*-simple groups (in Wesolek's sense).

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arXiv2021

Non-amenable tight squeezes by Kirchberg algebras

We give a framework to produce C*-algebra inclusions with extreme properties. This gives the first constructive nuclear minimal ambient C*-algebras. We further obtain a purely infinite analogue of Dadarlat's modeling theorem on AF-algebras: Every Kirchberg algebra is rigidly and KK-equivalently sandwiched by non-nuclear C*-algebras without intermediate C*-algebras. Finally we reveal a novel property of Kirchberg algebras: They embed into arbitrarily wild C*-algebras as rigid maximal C*-subalgebras.

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arXiv2021

Equivariant $\mathcal{O}_2$-absorption theorem for exact groups

We show that, up to strong cocycle conjugacy, every countable exact group admits a unique equivariantly $\mathcal{O}_2$-absorbing, pointwise outer action on the Cuntz algebra $\mathcal{O}_2$ with the quasi-central approximation property (QAP). In particular, we establish the equivariant analogue of the Kirchberg $\mathcal{O}_2$-absorption theorem for these groups.

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arXiv2020

The approximation property and exactness of locally compact groups

We extend a theorem of Haagerup and Kraus in the C*-algebra context: for a locally compact group with the approximation property (AP), the reduced C*-crossed product construction preserves the strong operator approximation property (SOAP). In particular their reduced group C*-algebras have the SOAP. Our method also solves another open problem: the AP implies exactness for general locally compact groups.

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arXiv2019

On pathological properties of fixed point algebras in Kirchberg algebras

We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group $Γ$ and any infinite group $Λ$, we construct an outer action of $Λ$ on the Cuntz algebra $\mathcal{O}_2$ whose fixed point algebra is almost equal to the reduced group C*-algebra ${\rm C}^\ast_{\rm r}(Γ)$. Moreover, we show that every infinite group admits outer actions on all Kirchberg algebras whose fixed point algebras fail the completely bounded approximation property.

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arXiv2019

Rigid sides of approximately finite dimensional simple operator algebras in non-separable category

Applying Popa's orthogonality method to a new class of groups, we construct amenable group factors which are prime and have no infinite dimensional regular abelian *-subalgebras. By adjusting Farah--Katsura's solution of Dixmier's problem to the von Neumann algebra setting, we obtain the first examples of prime AFD factors and tensorially prime simple AF-algebras. Our results are proved in ZFC, thus in particular answering questions asked by Farah--Hathaway--Katsura--Tikuisis. We also directly determine central sequences of certain crossed products. This concludes the failure of the Kirchberg $\mathcal{O}_\infty$-absorption theorem in the non-separable setting.

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arXiv2019

Complete descriptions of intermediate operator algebras by intermediate extensions of dynamical systems

Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely describe all intermediate operator algebras: the Galois Correspondence Theorem and the Tensor Splitting Theorem. Here we establish the third, new complete description theorem which gives a canonical bijective correspondence between intermediate operator algebras and intermediate extensions of dynamical systems. One can also regard this theorem as a crossed product splitting theorem, analogous to the Tensor Splitting Theorem. We then give concrete applications, particularly to maximal amenability problem and a new realization result of intermediate operator algebra lattice.

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arXiv2018

Almost finiteness for general etale groupoids and its applications to stable rank of crossed products

We extend Matui's notion of almost finiteness to general etale groupoids and show that the reduced groupoid C*-algebras of minimal almost finite groupoids have stable rank one. The proof follows a new strategy, which can be regarded as a local version of the large subalgebra argument. The following three are the main consequences of our result. (i) For any group of (local) subexponential growth and for any its minimal action admitting a totally disconnected free factor, the crossed product has stable rank one. (ii) Any countable amenable group admits a minimal action on the Cantor set all whose minimal extensions form the crossed product of stable rank one. (iii) For any amenable group, the crossed product of the universal minimal action has stable rank one.

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arXiv2018

Simple equivariant C*-algebras whose full and reduced crossed products coincide

For any second countable locally compact group G, we construct a simple G-C*-algebra whose full and reduced crossed product norms coincide. We then construct its G-equivariant representation on another simple G-C*-algebra without the coincidence condition. This settles two problems posed by Anantharaman-Delaroche in 2002. Some constructions involve the Baire category theorem.

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arXiv2016

Elementary constructions of non-discrete C*-simple groups

Recently Raum has given the first examples of locally compact non-discrete groups with the simple reduced group C*-algebra, answering a question of de la Harpe. Here we construct such groups whose proof relies only on results in the discrete case.

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