M. Anoussis, A. Katavolos, I. G. Todorov
In this work we characterise the C*-algebras A generated by projections with the property that every pair of projections in A has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property is equivalent to a lattice theoretic property of projections and also to the property that the set of finite-dimensional *-subalgebras of A is directed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We characterise the strictly closed left invariant C*-subalgebras of the C*-algebra C_b(G) of bounded continuous functions on a locally compact group G. On the dual side, we characterise the strictly closed invariant C*-subalgebras of the multiplier algebra of the reduced group C*-algebra C*_r(G) when G is amenable. In both cases, these C*-subalgebras correspond to closed subgroups of G.
A note on the orbit equivalence of injective actions
本文用对偶作用的简约交叉积刻画了离散可数Ore半群单射作用的变换广群C*-代数，并借助变换广群及其简约C*-代数刻画了连续轨道等价与半群紧致化上的单射作用。
We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the periodicity group of the graph. The groupoid of the k-graph then acts on the cartesian product of the infinite-path space of the graph with the dual group of the centre of any bicharacter representing this second-cohomology class. The twisted k-graph algebra is simple if and only if this action is minimal. We apply this result to characterise simplicity for many twisted crossed products of k-graph algeb…
We characterise quasidiagonality of the $C^*$-algebra of a cofinal $k$-graph in terms of an algebraic condition involving the coordinate matrices of the graph. This result covers all simple $k$-graph $C^*$-algebras. In the special case of cofinal $2$-graphs we further prove that AF-embeddability, quasidiagonality and stable finiteness of the $2$-graph algebra are all equivalent.
To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of groups on the boundary of its Bass-Serre tree. We characterise when this action is minimal, and find a sufficient condition under which it is locally contractive. In the case of generalised Baumslag-Solitar graphs of groups (graphs of groups in which every group is infinite cyclic) we also characterise topological freeness of this action. We are then able t…
Geometric Phases Characterise Operator Algebras and Missing Information
本研究建立几何相位与von Neumann代数的直接关联，证明零几何相位对应代数上存在良定义迹泛函，非零相位对应局域观测者的信息缺失，并结合AdS/CFT永恒黑洞等多个实例验证了结论。
We introduce the notion of $Δ$ and $σ\,Δ-$ pairs for operator algebras and characterise $Δ-$ pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of $Δ$-Morita equivalent operator spaces and prove a similar theorem about their algebraic extensions. We prove that $σΔ$-Morita equivalent operator spaces are stably isomorphic and vice versa. Finally, we study unital operator spaces, emphasising their left (resp. right) multiplier algebras, and prove theorems that refer to $Δ$-Morita equivalence of their algebraic extensions.
Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: (i) for many simple C$^*$-algebras, the Thomsen semigroup is recovered functorially from the Elliott invariant, and this yields a new proof of Elliott's classification theorem for simple, unital AI algebras; (ii) for the algebras in (i), classification of their Hilbert modules is similar to the von Neumann algebra context; (iii) for the algebras in (i), approximate unitary equivalence of self-adjoint operators is characterised in terms of the Elliott invariant.
Angles Between Intermediate Operator Subalgebras
本文引入了中间算子子代数之间的内角概念，并展示了其在非单位C*代数中的稳定性。
Operator systems, contextuality and non-locality
引入普适于情境性场景概率模型的算子系统，通过超图C*-代数刻画膨胀场景与无信号概率模型，并给出Connes嵌入问题的等价表述。
On possible values of the interior angle between intermediate subalgebras
研究证明了中间子代数内角可在$[0,\frac{\pi}{2}]$区间内取到，并计算了交叉积子代数之间的内角。
On dense subalgebras of the singular ideal in groupoid C*-algebras
研究群oid C*-代数中奇异理想稠密子代数的确定性，通过同态纤维性质和有限- nilpotent同态群的C*-代数密度特性进行分析。
It has already been established that the properties required of an abstract sequential product as introduced by Gudder and Greechie are not enough to characterise the standard sequential product $a\circ b = \sqrt{a}b\sqrt{a}$ on an operator algebra. We give three additional properties, each of which characterises the standard sequential product on either a von Neumann algebra or a Euclidean Jordan algebra. These properties are (1) invariance under application of unital order isomorphisms, (2) symmetry of the sequential product with respect to a certain inner product, and (3) preservation of in…
Delocalised traces on Hecke algebras of right-angled, hyperbolic type
研究在右角双曲类型Hecke C*代数中构造平滑子代数，使与关联Coxeter群中任意共轭类相关的追踪可扩展，并计算由此产生的去局域化追踪与K理论的配对，证明其在K理论上忠实。
A geometric characterisation of real C*-algebras
本文从几何角度刻画实C*-代数，证明其正锥内部恰为具有可定向扩张的Finsler对称锥，并等价于空间作为单位实C*-代数埃尔米特部分的范数等价条件。
In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more general, vector valued case. This method is used to analyze the traces of the Hecke operators. We construct representations of the Hecke algebra of a group $G$, relative to an almost normal subgroup $Γ$, into the von Neumann algebra of the group $G$, tensor matrices. The representations we obtain are a lifting of the Hecke operators to this larger algebra. …
Von Neumann entropy of the angle operator between a pair of intermediate subalgebras
本文研究简单 C*-代数单位包含中一对中间子代数之间的夹角算子，并针对一大类四元组给出了其对偶夹角算子冯·诺依曼熵的可计算公式。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。