Related papers: Semidirect Product of Groupoids, Its Representatio…

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the…

Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was…

We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introduced in the thesis of S.~Roy and, unlike the investigations…

Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…

The unitary irreducible representations of a Lie group defines the Hilbert space on which the representations act. If this Lie group is a physical quantum dynamical symmetry group, this Hilbert space is identified with the physical quantum…

We investigate here various kinds of semi-product subgroups of Poincar\'e group in the scheme of Cohen-Glashow's very special relativity along the deformation approach by Gibbons- Gomis-Pope. For each proper Poincar\'e subgroup which is a…

We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $\Gamma$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under…

Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the…

We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are defined on groupoids whose algebroid can be endowed with a…

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…

An abstract sampling theory associated to a unitary representation of a countable discrete non abelian group $G$, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples…

In this paper, we have studied the loops which are the semidirect products of a loop and a group. Also, the cummutant, nuclei and the center of such loops are studied.

The recently developed theory of partial actions of discrete groups on $C^*$-algebras is extended. A related concept of actions of inverse semigroups on $C^*$-algebras is defined, including covariant representations and crossed products.…

We define a semidirect product groupoid of a system of partially defined local homeomorphisms $T=(T_{1},..., T_{r})$. We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use…

Groupoids are the oidification of groups, and they are largely used in topology and representation theory. We consider here the category $\mathsf{Gpd}$ of all groupoids with all morphisms, and the category $\mathsf{Gpd}_\Lambda$ of…

Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C*-algebras and Hilbert bimodules. The essential point is that whenever one…

We give an algebraic/geometric characterization of the classical pseudodifferential operators on a smooth manifold in terms of the tangent groupoid and its natural $\mathbb{R}^\times_+$-action. Specifically, we show that a properly…

Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…

Geodesics and curvature of semidirect product groups with right invariant metrics are determined. In the special case of an isometric semidirect product, the curvature is shown to be the sum of the curvature of the two groups. A series of…

This work is devoted to the study of Bessel and Riesz systems of the type $\big\{L_{\gamma}\mathsf{f}\big\}_{\gamma\in \Gamma}$ obtained from the action of the left regular representation $L_{\gamma}$ of a discrete non abelian group…