In this paper, we introduce transposition regularity into AG-groupoids, and a variety of regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties structures discussed by their decomposition theorems: (1) L1/R1-transposition equivalent to each other, they can be decomposed the union disjoint Abelian subgroups; (2) LR-transposition an example is given illustrate that ...

This paper is concerned with the algebraic structure of groupoids and crossed modules of groupoids. We describe the group structure of the automorphism group of a finite connected groupoid C as a quotient of a semidirect product. We pay particular attention to the conjugation automorphisms of C, and use these to define a new notion of groupoid action. We then show that the automorphism group of...

In this note a functorial approach to the integration problem of an LAgroupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibered products in the categories of Lie groupoids and Lie algebroids, giving necessary and sufficient conditions for the existence of such. In particular, it turns out, that the fibered product of Lie algebroids along integrable morphisms is...

We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain complete characterization congruence-simpleness for Steinberg algebras second-countable groupoids, extending well-known characterizations when S is field. apply our congruence-simplicity results to tight groupoids inverse semigroup representations associated self-similar graphs.

We start by describing the relationship between the classical prequantization condition and the integrability of a certain Lie algebroid associated to the problem and use this to give a global construction of the prequantizing bundle in terms of path spaces (Introduction), then we rephrase the problem in terms of groupoids (second section), and then we study the more general problem of prequant...