Related papers: Boutet de Monvel's Calculus and Groupoids I

Let $\ell$ be a length function on a group G, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a…

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 \lambda. The twisted groupoid C*-algebra C*(E;G,\lambda) is a quotient of the C*-algebra…

We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…

Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. We show that its $C^*$-closure is an extension of a noncommutative algebra of principal…

For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have `geometric K-theory', namely the `transmission algebra' introduced by Boutet de Monvel, the `zero algebra' introduced by Mazzeo and…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

Let A denote the smallest C*-subalgebra of the algebra of all bounded operators on L^2(R) containing: (i) all multiplications a(M) by functions a in C[-\infty,+\infty], (ii) all multiplications e^{ijM}, j in Z, and (iii) all operators of…

In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system $(\mathcal{B},\mathcal{L}, \theta, \mathcal{I}_{\alpha})$. For the first groupoid, we associate an inverse semigroup to a generalized…

Let $G$ be a locally compact group and $P \subset G$ be a closed Ore semigroup containing the identity element. Let $V: P \to B(\clh)$ be a representation such that for every $a \in P$, $V_{a}$ is an isometry and the final projections of…

The notion of a self-similar ultragraph $(G,\mathcal{U},\varphi)$ and its $C^*$-algebra $\mathcal{O}_{G,\mathcal{U}}$ were introduced in our recent work, where we proposed inverse semigroup and groupoid models for such $C^*$-algebras as…

Let $P=G/K$ be a semisimple non-compact Riemannian symmetric space, where $G=I_0(P)$ and $K=G_p$ is the stabilizer of $p\in P$. Let $X$ be an orbit of the (isotropy) representation of $K$ on $T_p(P)$ ($X$ is called a real flag manifold).…

In this paper we give an example of a proper standard C*-algebra (a proper C*-subalgebra of B(H) containing C(H)) whose automorphism and isometry groups are topologically reflexive. Furthermore, we prove that in the case of extensions of…

Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into…

Given a Hausdorff locally compact \'etale groupoid $\mathcal G$, we describe as a topological space the part of the primitive spectrum of $C^*(\mathcal G)$ obtained by inducing one-dimensional representations of amenable isotropy groups of…

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman…

Work of Jean Renault shows that, for topologically principal \'etale groupoids, a diagonal-preserving isomorphism of reduced $C^*$-algebras yields an isomorphism of groupoids. Several authors have proved analogues of this result for ample…

In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We will show that a global pseudo-differential calculus can be…

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…

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows…

Let $G$ be a simply connected solvable Lie group with a lattice $\Gamma$ and the Lie algebra $\g$ and a representation $\rho:G\to GL(V_{\rho})$ whose restriction on the nilradical is unipotent. Consider the flat bundle $E_{\rho}$ given by…