By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a oneobject 2-group. By a permutation 2-group we mean the 2-group Sym(G) of self-equivalences of a groupoid G and natural isomorphisms between them, with the product given by composition of self-equivalences. These generalize the ...

For any body-time manifold [Formula: see text] there exists a groupoid, called the material encoding all properties of evolution. A smooth distribution, is constructed to deal with case in which groupoid not Lie groupoid. This new tool provides unified framework general non-uniform

X iv :0 80 3. 04 72 v1 [ m at h. R A ] 4 M ar 2 00 8 On decomposition of commutative Moufang groupoids B.V.Novikov It is well-known that the multiplicative groupoid of an alternative/Jordan algebra satisfies Moufang identities [1, 4]. Therefore it seems interesting to study the structure of such groupoids. In this note we apply to Moufang groupoids an approach which is widespread in Semigroup T...

In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group G with dual G⋆ we obtain a suitably connected integrating symplectic double groupoid S. As a consequence, the cotangent lift of a Poisson action on an integrable Poisson manifold P can be integrated to a Poisson actio...

We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.

We investigate finite commutative groupoids G = 〈G, ◦〉 such that g ◦ h 6= g for all elements g, h of G. First, we show that for any such groupoid, its weak (i.e. partial) subgroupoid lattice uniquely determines its subgroupoid lattice. Next, we characterize the lattice of all weak subgroupoids of such a groupoid. This is a distributive finite lattice satisfying some combinatorial conditions con...

In a recent paper of Tamura, Merkel, and Latimer [2], the following question was raised: Suppose 5 is a groupoid (cf. [l]) which satisfies: (1) There is at least one left identity in S. (2) If y or z is a left identity of 5, then x(yz) =■= (xy)z for all xES. (3) For all a, bES there exists x£5 such that ax = b. Then does S satisfy: (3') For any xES there is a unique left identity e (which may d...

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 ...

We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault–Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault– Deaconu groupoid itself. We also show that when the bundle is locally compact the associated C∗-algebra is primitive and has a densely defin...