M. R. Buneci, P. Stachura
The purpose of this paper is extend the notion of morphism of groupoids introduced by Zakrzewski to locally compact $σ$-compact groupoids endowed with Haar systems and to use the extension to construct a covariant functor from this category to a category of $C^{\ast}$-algebras in the sense of Woronowicz.
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 shall consider a locally compact groupoid endowed with a Haar system and having proper orbit space. We shall construct a groupoid C*-algebra which is independent of the Haar system (up to a *-isomorphism).
For second countable locally compact Hausdorff groupoids, the property of possessing a Haar system is preserved by equivalence.
It is shown that a locally compact groupoid with open range map does not always admit a Haar system. It then is shown how to construct a Haar system if the stability groupoid and the quotient by the stability groupoid both admit one.
We consider groupoids on $\{1,2,..,d\}^\mathbb{N}$, cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We assume a mild compatibility of the groupoid with the symbolic structure. We present a generalization of the Ruelle operator - the Haar-Ruelle operator - taking into account the Haar structure. We consider continuous and also Hölder cocycles. IFS with weights appears in our reasoning in the Hölder case.
Topological fundamental groupoid. III. Haar systems on the fundamental groupoid
本文研究道路连通、局部道路连通且半局部单连通空间的基本群胚上 Haar 系的存在性与描述，给出等价判据、C*代数描述及两个测度公式。
Induced Representation of Topological groupoids
介绍局部紧第二可数群胚\(G\)从闭宽子群胚\(H\)的连续酉表示的诱导表示，证明其基本性质、分步诱导定理等，还给出群胚版麦基张量积定理及紧可迁群胚版弗罗贝尼乌斯互反定理。
If $G$ is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.
We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide a plethora of examples of Haar system preserving morphisms and discuss connections to noncommutative CW-complexes and interval algebras. We prove that an inverse system of groupoids with Haar system preserving bonding maps has a limit, and that we get a corresponding direct system of groupoid $C^*$-algebras. An explicit construction of an inverse system of …
We analyse certain Haar systems associated to groupoids obtained by certain natural equivalence relations of dynamical nature on sets like $\{1,2,...,d\}^\mathbb{Z}$, $\{1,2,...,d\}^\mathbb{N}$, $S^1\times S^1$, or $(S^1)^\mathbb{N}$, where $S^1$ is the unitary circle. We also describe properties of transverse functions, quasi-invariant probabilities and KMS states for some examples of von Neumann algebras (and also $C^*$-Algebras) associated to these groupoids. We relate some of these KMS states with Gibbs states of Thermodynamic Formalism. While presenting new results, we will also describe …
Suppose G is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids, and show G is integrable if and only if the groupoid C*-algebra C*(G) has bounded trace.
Let $G$ be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem by Clark about GCR groupoid $C^*$-algebras. We show that if the groupoid $C^*$-algebra of $G$ is GCR then the orbits of $G$ are locally closed.
In this paper, we consider topological semigroup actions on compact topological spaces. Under mild assumptions on the semigroup and the action, we construct a semi-direct product groupoid with a Haar system. We also show that it is equivalent to a transformation groupoid. We apply this construction to the Wiener-Hopf $C^{*}$-algebras.
Let G be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem of Clark about groupoids whose $C^*$-algebras are CCR. We show that if the groupoid C*-algebra of G is CCR then the orbits of G are closed.
Let $(G,α)$ and $(H,β)$ be locally compact groupoids with Haar systems. We define a topological correspondence from $(G,α)$ to $(H,β)$ to be a $G$-$H$-bispace $X$ on which $H$ acts properly and $X$ carries a continuous family of measures which is $H$-invariant and each measure in the family is $G$-quasi invariant. We show that a topological correspondence produces a $C^*$-correspondence from $C^*(G,α)$ to $C^*(H,β)$. We give many examples of topological correspondences.
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.
Let $G$ be a second countable, locally compact groupoid with Haar system, and let $\mathcal{A}$ be a bundle of $C^{\ast}$-algebras defined over the unit space of $G$ on which $G$ acts continuously. We determine conditions under which the associated crossed product $C^{\ast}(G;\mathcal{A})$ is a continuous trace $C^{\ast}$-algebra.
Von Neumann algebras as reduced twisted groupoid $C^*$-algebras
本文刻画了同构于约化扭曲群胚$C^*$-代数的冯·诺依曼代数，证明其为次齐次代数，并引入受控传播障碍，排除$B(H)$及Calkin代数的嵌入。
Let G be a second-countable locally-compact Hausdorff groupoid with a Haar system, and let {x_n} be a sequence in the unit space of G. We show that the notions of strength of convergence of {x_n} in the orbit space and measure-theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid C*-algebra.
Let E be a second-countable, locally compact, Hausdorff groupoid equipped with an action of T such that G:=E/T is a principal groupoid with Haar system λ. The twisted groupoid C*-algebra C*(E;G,λ) is a quotient of the C*-algebra of E obtained by completing the space of T-equivariant functions on E. We show that C*(E;G,λ) is postliminal if and only if the orbit space of G is T_0 and that C*(E;G, λ) is liminal if and only if the orbit space is T_1. We also show that C*(E;G, λ) has bounded trace if and only if G is integrable and that C*(E;G, λ) is a Fell algebra if and only if G is Cartan. Let \…
Amenable unitary representations of locally compact groupoids
本文研究局部紧群体的可约酉表示，通过Hilbert束理论和算子值向量测度定义拓扑不变均值，将Bekka对群的可约性刻画推广到群体。
This article extends the main results of the publication arXiv:2001.01312 to the case of a twisted groupoid. More precisely, it gives a decomposition of the C*-algebra of a twisted locally compact groupoid with Haar system in presence of a normal subgroupoid. When the normal subgroupoid and the twist over it are abelian, one obtains another twisted groupoid C*-algebra. This is applied to C*-algebraic deformation quantization and to multiplier representations of locally compact abelian groups.
We extend the symbol calculus and study the limit operator theory for $σ$-compact, étale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact groups and discrete metric spaces with Property A, but also establish new limit operator theories for group/groupoid actions and uniform Roe algebras of groupoids. In the process, we extend a monumental result by Exel, Nistor and Prudhon, showing that the invertibility of an element in the groupoid $C^*$-algebra of a $σ$-compact amenable groupoid with a Haar system is …
We introduce the concept of Roe C*-algebra for a locally compact groupoid whose unit space is in general not compact, and that is equipped with an appropriate coarse structure and Haar system. Using Connes' tangent groupoid method, we introduce an analytic index for an elliptic differential operator on a Lie groupoid equipped with additional metric structure, which takes values in the K-theory of the Roe C*-algebra. We apply our theory to derive a Lichnerowicz type vanishing result for foliations on open manifolds.
Suppose $G$ is a second countable, locally compact Hausdorff groupoid with abelian stabilizer subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid $C^*$-algebra to have Hausdorff spectrum. In particular we show that the spectrum of $C^*(G)$ is Hausdorff if and only if the stabilizers vary continuously with respect to the Fell topology, the orbit space $G^{(0)}/G$ is Hausdorff, and, given convergent sequences $χ_i\to χ$ and $γ_i\cdotχ_i \to ω$ in the dual stabilizer groupoid $\hat{S}$ where the $γ_i\in G$ act via conjugation, if $χ$ and $ω$ are elements o…
Almost Representations of Groupoids on Banach Bundles
本研究将紧群几乎表示的经典结果推广到带连续Haar测度系统的真群胚，证明其在有限秩Hilbert丛上局部有足够多连续表示，进而得到纯拓扑下群胚的Tannaka对偶新推广。
Let $(G,α)$ and $(H,β)$ be locally compact Hausdorff groupoids with Haar systems, and let $(X,λ)$ be a topological correspondence from $(G,α)$ to $(H,β)$ which induce the ${C}^*$-correspondence $\mathcal{H}(X)\colon {C}^*(G,α)\to {C}^*(H,β)$. We give sufficient topological conditions which when satisfied the ${C}^*$-correspondence $\mathcal{H}(X)$ is proper, that is, the ${C}^*$-algebra ${C}^*(G,α)$ acts on the Hilbert ${C}^*(H,β)$-module ${H}(X)$ via the comapct operators. Thus a proper topological correspondence produces an element in ${KK}({C}^*(G,α),{C}^*(H,β))$.
We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real Čech cohomology, which is an equivariant-like cohomology theory suitable for the context of groupoids with involutions. The Picard group of such a groupoid is discussed and is given a cohomological picture. Eventually, we generalize Crainic's result, about the differential cohomology of a proper Lie groupoid with coefficients in a given representation, to the topological case.
If $G$ is a locally compact groupoid with a Haar system $λ$, then a positive definite function $p$ on $G$ has a form $p(x)=< L(x)ξ(d(x)),ξ(r(x))>$, where $L$ is a representation of $G$ on a Hilbert bundle ${\h}=(G^0,\{H_u\},μ)$, $μ$ is a quasi invariant measure on $G^0$ and $ξ\in L^{\infty}(G^0,{\h})$. [10]. In this paper firt we prove that if $μ$ is a quasi invariant ergodic measure on $G^0$, then two corresponding representations of $G$ and $C_c(G)$ are irreducible in the same time. Then by using the theory of positive linear functionals on $C^*(G)$ we show that when $μ$ is an ergodic quasi …
We establish that a second countable locally compact groupoid possessing a continuous Haar system is topologically amenable if and only if it is Borel amenable. We give some examples and applications.
The Unitary Conjugation Groupoid of a Type I C*-Algebra: Topology, Fell Continuity, and the Canonical Diagonal Embedding
本文提出了一种基于II型C*-代数的规范群oid构造，通过规范对角嵌入将代数嵌入到群oidC*-代数中，展示了其在K-理论和拓扑学中的应用。
We construct a new class of finite-dimensional C^*-quantum groupoids at roots of unity q=e^{iπ/\ell}, with limit the discrete dual of the classical SU(N) for large orders. The representation category of our groupoid turns out to be tensor equivalent to the well known quotient C^*-category of the category of tilting modules of the non-semisimple quantum group U_q({\mathfrak sl}_N) of Drinfeld, Jimbo and Lusztig. As an algebra, the C^*-groupoid is a quotient of U_q({\mathfrak sl}_N). As a coalgebra, it naturally reflects the categorical quotient construction. In particular, it is not coassociati…
We review various notions of correspondences for locally compact groupoids with Haar systems, in particular a recent definition due to R.D. Holkar. We give the construction of the representations induced by such a correspondence. Finally, we extend the construction of induced representations to hypergroupoids.
In the previous article, we proved that a topological correspondence $(X,λ)$ from a locally compact groupoid with a Haar system $(G,α)$ to another one, $(H,β)$, produces a $C^*$-correspondence $\mathcal{H}(X)$ from $C^*(G,α)$ to $C^*(H,β)$. In the present article, we describe how to form a composite of two topological correspondences when the bispaces are Hausdorff and second countable in addition to being locally compact.
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。