We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

in this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. we show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian stabilizers and a well behaved orbit space. In this case, the spectrum of the crossed product is homeomorphic, via an induction map, to a quotient of the spe...

It is shown that a central extension of a Lie groupoid by an Abelian Lie group A has a principal A-bundle structure and the extended Lie groupoid is classified by an Euler esclass. Then we prove that for a symplectic α-connected, αβtransversal or α-simply connected groupoid, there exists at most one central S-extension, the Euler es-class of which corresponds to the Poisson cohomology class of ...

Tarski associative groupoid (TA-groupoid) is a kind of non-associative satisfying law. In this paper, the new notions transposition regular TA-groupoid are proposed and their properties structural characteristics studied by using band quasi-separativity. particular, following conclusions strictly proved: (1) every left semigroup; (2) disjoint union sub Abelian groups; (3) finite with quasi-sepa...

Our main aim is to associate a holonomy Lie groupoid to the connective structure of an abelian gerbe. The construction has analogies with a procedure for the holonomy Lie groupoid of a foliation, in using a locally Lie groupoid and a globalisation procedure. We show that path connections and 2–holonomy on line bundles may be formulated using the notion of a connection pair on a double category,...

Central S-extensions of the fundamental groupoid of a connected symplectic manifold with an Abelian fundamental group, satisfying some conditon on the universal covering space are computed.

This is a sequel to the paper [6] ‘Homology of types in model theory I: Basic concepts and connections with type amalgamation’. We compute the group H2 for strong types in stable theories and show that any profinite abelian group can occur as the group H2 in the model-theoretic context. The work described in this paper was originally inspired by Hrushovski’s discovery [8] of striking connection...

Given a normal subgroup bundle A of the isotropy groupoid ?, we obtain twisted action quotient ?/A on group C?-algebras determined by whose crossed product recovers C?-algebra C?(?). Restricting to case where is abelian, describe C?(?) as associated T-groupoid over tranformation obtained from canonical Pontryagin dual space A. We give some illustrative examples this result.