Marius Dadarlat
It is shown that a separable exact residually finite dimensional C*-algebra with locally finitely generated (rational) even K-homology embeds in a uniformly hyperfinite C*-algebra.
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Amalgamated free products of commutative C*-algebras are residually finite-dimensional
证明了可分交换C* 代数的合并自由积是剩余有限维的。
Primitivity of unital full free products of residually finite dimensional C*-algebras
一个C* 代数称为本原的，如果它允许一个忠实的和不可约的 *-表示.本文证明了：如果A_1和A_2是可分的、有单位的、剩余有限维的C* 代数-代数，且不都是二维的，则它们的有单位的C*-代数全自由积A = A_1*A_2是本原的.由此得出A是反阈的，并且纯态集在状态空间中是w* 稠密的。
Couniversality for C*-algebras of residually finite-dimensional operator algebras
本文研究了附着于固定算子代数的剩余有限维（RFD）C*-代数空间中的余泛存在性，构造了不存在最小RFD C*-代数的实例，并证明了在大量张量代数和圆盘代数情形下RFD C*-代数空间在C*-覆盖下确界下不封闭。
We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of finite-dimensional $\mathrm{C}^*$-algebras, in the non-selfadjoint setting we show that an additional level of flexibility must be allowed. Motivated by this peculiarity, we consider a natural non-selfadjoint notion of residual finite-dimensionality. We identify sufficient conditions for the tensor algebra of a $\mathrm{C}^*$-correspondence to enjoy this property. To clarify the connection with the usual self-adjoint n…
Entropy for expansive algebraic actions of residually finite groups
本文证明了剩余有限群的扩张主代数作用的sofic熵的一个公式，推广了Deninger和Schmidt最近的工作。
Just-infinite C*-algebras, i.e., infinite dimensional C*-algebras, whose proper quotients are finite dimensional, were investigated in [Grigorchuk-Musat-Rordam, 2016]. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in that article. In this paper we extend that construction by showing that each infinite dimensional metrizable Choquet simplex is affinely homeomorphic to the trace simplex of a just-infinite residually finite dimensional C*-algebras. The trace simplex of any unital residually finite dimensional C*-algebra is hence realized by a …
Rokhlin dimension for actions of residually compact groups
本文提出残余紧致群作用的Rokhlin维度概念，研究其在交叉积下的保值性质及与动力系统管径维度的关系。
Operator spaces and residually finite-dimensional $C^\ast$-algebras
对于每个算子空间$X$，包含它的$C^\ast$ -代数是剩余有限维的（即，有一个分离的有限维表示族）。特别地，任何赋范空间上的自由$C^\ast$ -代数都是如此。这是Goodearl和Menal的早期结果的扩展，我们的简短证明是基于Exel和Loring的标准。
The von Neumann algebra of the non-residually finite Baumslag group < a,b | a b^3 a^-1 = b^2 > embeds into R^omega
本文分析了有限vonNeumann代数M中某些元素的非交换矩集的结构。若M的基本群是R +\{0}，则矩集是凸的;若M同构于M张量M，则矩集在点乘下是闭的.我们引入一类离散群，我们称之为超线性。这些是R^omega的酉群的离散子群（具有无限共轭类）。我们证明了这个类严格大于（i.c.c.）剩余有限群特别地，它包含Baumslag群< a，b| a b^3 a^-1 = b^2 >。这导致了一个先前未知的（非超有限的）II_1型因子，它可以嵌入R^omega。这是康纳斯猜想的积极证据，即任何可分离的II_1因子都可以嵌入R^omega。
On the permanence properties of residually exact groups
本文研究了余精确群的持久性性质，证明其在图积、双同化积和特殊HNN扩展下保持闭合。
Expansive algebraic actions of discrete residually finite amenable groups and their entropy
利用紧阿贝尔群在Fuglede-Kadison行列式下的自同构，证明了可数离散剩余有限群$Γ$的某些扩张作用的熵公式.这扩展了第一作者在限制性更强的条件下证明的一个较早的结果。这一推广的主要工具是一个表示的$Γ$ -行动的一个“基本同宿点”，和熵的描述方面的重整化对数增长率的一组$Γ_n$ -不动点，其中$(Γ_n, n\ge1)$是一个递减序列的有限指数正规子群的$Γ$平凡的交集。
Residually Finite Partial Actions and MF Fell Bundles
本文研究Fell丛和偏C*-动力系统构建的截面C*-代数的MF性质与拟对角性，将剩余有限作用概念推广至偏拓扑动力系统，并证明偏Bernoulli移位在特定群条件下产生MF约化交叉积。
We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$ coacting universally on an $n$-dimensional Hilbert space has enough finite-dimensional representations in the sense that every non-zero element acts non-trivially in some finite-dimensional *-representation. This implies that the discrete quantum group with group algebra $A_u(n)$ is maximal almost periodic (i.e. it embeds in its quantum Bohr compactification), answering a question posed by P. So tan. We also prove analogous results for the involutive Hopf *-algebra $B_u(n)$ coacting universally on an $n$-dimensional Hilbert…
Residually finite actions and crossed products
本文研究了紧T2空间上离散群连续作用的剩余有限性的概念，以及它与约化交叉积的范数微观态的存在性的关系。我们的主要结果是：零维紧致可度量化空间上的自由群的作用是剩余有限的当且仅当它的约化交叉积容许范数微观态，即，是MF代数。
We give a construction of a family of locally finite residually finite groups with just-infinite C*-algebra. This answers a question from [2]. Additionally, we show that residually finite groups of finite exponent are never just-infinite.
We introduce the concept of Rokhlin dimension for actions of residually finite groups on C*-algebras, extending previous notions of Rokhlin dimension for actions of finite groups and the integers, as introduced by Hirshberg, Winter and the third author. If the group has a box space of finite asymptotic dimension, then actions with finite Rokhlin dimension preserve the property of having finite nuclear dimension, when passing to the crossed product C*-algebra. A detailed study of the asymptotic dimension of box spaces shows that finitely generated, virtually nilpotent groups have box spaces wit…
The RFD and KAC quotients of the Hopf*-algebras of universal orthogonal quantum groups
本文确定了普适正交量子群相关Hopf *-代数的Kac商与RFD商，揭示了其结构性质。
The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra $A$ has abelian central sequence algebra if and only if A satisfies Fell's condition. Moreover, we introduce a higher-dimensional analogue of Fell's condition and show that it completely characterizes subhomogeneity of central sequence algebras. In contrast, we show that any non-trivial extension by compact operators has not only non-abelian but not even resid…
Homotopy invariance of AF-embeddability
证明了AF-可嵌入性是可分正合$C^*$ -代数类中的同伦不变量。本文的工作受到Spielberg关于AF-可嵌入性的同伦不变性的工作和Dadarlat关于剩余有限维$C^*$ -代数的AF-可嵌入性的系列工作的启发。
The RFD property for graph $C^*$-algebras
研究图C*代数的RFD性质，证明其当且仅当图无无限接收点、无带退出的环、无无限反向链，并且每个顶点都能通过有限路径到达汇点或环或无限发射点。
We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator algebras, and we provide an affirmative answer for representations whose range is residually finite-dimensional. Furthermore, we show that weak-${}^*$ closed, amenable, residually finite-dimensional operator algebras are similar to $C^*$-algebras, and in particular have the property that all their bounded representations are completely bounded. We prove our results…
On embeddings of full amalgamated free product C*-algebras
研究了由C* 代数A在A '中，B在B'中，D在D '中的相容包含所产生的全合并自由积C* 代数-代数λ：A *_DB--> A' *_{D '} B'的 *-同态何时是嵌入的问题.给出了λ是单射的充分条件，以及λ不是单射的例子类.作为应用，我们给出了有限维C* 代数的全合并自由积是剩余有限维的充要条件.
Lifting algebraic contractions in C*-algebras
设p为单变量一元多项式。证明了关系p（x）=0，|x | \le C的泛C* 代数是半投射的，剩余有限维的，有平凡扩张群.
We prove that pushouts $A*_CB$ of residually finite-dimensional (RFD) $C^*$-algebras over central subalgebras are always residually finite-dimensional provided the fibers $A_p$ and $B_p$, $p\in \mathrm{spec}~C$ are RFD, recovering and generalizing results by Korchagin and Courtney-Shulman. This then allows us to prove that certain central pushouts of amenable groups have RFD group $C^*$-algebras. Along the way, we discuss the problem of when, given a central group embedding $H\le G$, the resulting $C^*$-algebra morphism is a continuous field: this is always the case for amenable $G$ but not in…
By analogy with the well-established notions of just-infinite groups and just-infinite (abstract) algebras, we initiate a systematic study of just-infinite C*-algebras, i.e., infinite dimensional C*-algebras for which all proper quotients are finite dimensional. We give a classification of such C*-algebras in terms of their primitive ideal space that leads to a trichotomy. We show that just-infinite, residually finite dimensional C*-algebras do exist by giving an explicit example of (the Bratteli diagram of) an AF-algebra with these properties. Further, we discuss when C*-algebras and *-algebr…
Quasidiagonal traces need not form a face
本文构造了一个可分单位剩余有限维C*-代数，其拟对角迹不构成迹态空间的面，通过加权表示阶梯连接两个副本并证明拟对角迹对两副本等权。
Semiprojectivity of universal C*-algebras generated by algebraic elements
设$p$是一个单变量一元多项式，其根的重数要么都大于1，要么都恰好为1。证明了关系$p(x)=0$，$\|x\| \le 1$的泛$C^*$ -代数是半投射的.在所有根重的情况下，证明了泛$C^*$ -代数也是剩余有限维的.应用多项式紧算子。
A quasidiagonal $C^*$-algebra with a nonquasidiagonal maximal tensor square
构造一个可分单幺剩余有限维 $C^*$-代数 $A$，其极大张量平方含真等距，从而 $A$ 拟对角线而 $A\ max A$ 非拟对角线，通过性质 $(T)$ 子群与膨胀共轭实现。
Nuclear dimension and virtually polycyclic groups
研究证明几乎多项式群的群C*-代数具有有限核维数，并提出相关猜想，同时给出首个有限生成非余有限群的此类例子。
A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an operator algebra is RFD if and only if every representation can be approximated by finite dimensional ones in the point weak operator topology. This is a non-self-adjoint version of a theorem of Exel and Loring for $C^*$-algebras. Moreover, we construct an example of an operator algebra for which approximation in the point strong operator topology is not possibl…
Embedding Dimensions of Finite von Neumann Algebras
当von Neumann代数可以忠实地嵌入到超有限II $_1$因子的超幂中时，我们引入了有限von Neumann代数的生成元族的“嵌入维数”.这些嵌入维数是冯诺依曼代数不变量，即，不依赖于发电机的选择。我们还发现这些不变量的一些特定的冯诺依曼代数的值。
Algebraic reformulation of Connes embedding problem and the free group algebra
我们给出了I. Klep和M.通过考虑可数生成自由群的 *-代数，给出了Connes嵌入问题的Schweighe代数化.这允许只考虑酉生成元中的二次多项式，而不是自伴生成元中的任意多项式。
Entropy and the variational principle for actions of sofic groups
最近Lewis Bowen在容许有限熵生成划分的标准概率空间上引入了可数sofic群的保测度作用的熵概念。通过应用算子代数的角度来看，我们开发了一个更一般的方法，sofic熵产生测量和拓扑动力学不变量，我们建立了变分原理在这方面。在剩余有限群的情况下，利用变分原理计算了定义群环元在完全群C*-代数中可逆的主代数作用的拓扑熵.
We introduce the $C^*$-algebra $C^*(κ)$ generated by the Koopman representation $κ$ of an étale groupoid $G$ acting on a measure space $(X,μ)$. We prove that for a level transitive self-similar action $(G,E)$ with $E$ finite and $|uE^1|$ constant, there is an invariant measure $ν$ on $X=E^\infty$ and that $C^*(κ)$ is residually finite-dimensional with a normalized self-similar trace. We also discus $p$-fold similarities of Hilbert spaces in connection to representations of the graph algebra $C^*(E)$ and self-similar representations of $G$ in connection to the Cuntz-Pimsner algebra $C^*(G,E)$.
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to general (possibly non-self-adjoint) operator algebras. While numerous subtleties emerge in this greater generality, we exhibit novel tools for constructing finite-dimensional approximations. One such tool is a notion of a residually finite-dimensional coaction of a semigroup on an operator algebra, which allows us to construct finite-dimensional approxi…
Rokhlin Dimension: Permanence Properties and Ideal Separation
本文研究剩余有限群在 C*-代数上的作用的 Rokhlin 维数，给出等价定义，证明保持性质，并利用 Sierakowski 定理表明有限 Rokhlin 维数下约化交叉积的理想源于底层代数的不变理想。
We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An operator algebra may be RFD while simultaneously possessing completely isometric representations whose generating C*-algebra is not RFD. This has provided many hurdles in characterizing residual finite-dimensionality for operator algebras. To better understand the elusive behaviour, we explore the C*-covers of an operator algebra. First, we equate the collection of C*-covers with a complete lattice arising from the spectrum of the maximal C*-cover. This allows us to identify a largest RFD C*-cov…
Tensor algebras of subproduct systems and noncommutative function theory
本文重新研究无限维纤维子乘积系统的张量代数，刻画其可识别为非交换齐次簇上一致连续非交换函数代数的条件，指出无限维纤维情形下零点定理可能不成立，并解决了其同构问题。
We work on $\ell_p$ uniform Roe algebras associated to metric spaces, and on their mutual embedding. We generalize results of I. Farah and the authors to mutual embeddings of uniform Roe algebras of operators on $\ell_p$ spaces. Simultaneously, we obtain rigidity results for the classic uniform Roe $\mathrm{C}^*$-algebras which depend only on their Banach algebra structure.
In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces $X$ and $Y$, we are interested in which large scale geometric properties are stable under embedding of the uniform Roe algebra of $X$ into the uniform Roe algebra of $Y$.
Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.
We survey the model theoretic approach to a variety of ultrapower embedding problems in operator algebras.
Let $A$ be a separable, unital, simple, $\mathcal{Z}$-stable, nuclear $C^*$-algebra, and let $α\colon G\to \mathrm{Aut}(A)$ be an action of a countable amenable group $G$. If the trace space $T(A)$ is a Bauer simplex and the action of $G$ on $\partial_eT(A)$ has finite orbits and Hausdorff orbit space, we show that $α$ is strongly outer if and only if $α\otimes\mathrm{id}_{\mathcal{Z}}$ has the weak tracial Rokhlin property. If $G$ is moreover residually finite, then these conditions are also equivalent to $α\otimes\mathrm{id}_{\mathcal{Z}}$ having finite Rokhlin dimension (in fact, at most 2)…
Recursive Fermion System in Cuntz Algebra.I -- Embeddings of Fermion Algebra into Cuntz Algebra ---
利用递归构造方法，将费米子的CAR（正则反对易关系）代数嵌入到Cuntz代数${\cal O}_2$（或更一般的${\cal O}_{2d}$）中.作为一个典型的例子，我们显式地构造了CAR到${\cal O}_2$的U（1）-不变子代数上的嵌入.将这一构造推广到${\cal O}_{2^p}$的情形，得到了CAR在${\cal O}_{2^p}$的U（1）-不变子代数上的嵌入.限制Cuntz代数的一个置换表示，得到CAR的Fock表示.我们应用这些结果，按照Green定理把$p$阶的仿费米子代数嵌入到${\cal O}_{2^p}$中.
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