Abstract Motivated by the problem of characterizing KMS states on reduced C$^*$-algebras étale groupoids, we show that norm these algebras induces a C$^*$-norm group isotropy groups. This coincides with for transformation but, as follows from examples Higson–Lafforgue–Skandalis, it can be exotic already groupoids germs associated actions. We is still one some classes graded in particular, parti...

In 7] the notions of recognition by semigroups and by programs over semigroups were extended to groupoids. This led to a new characterization of the context-free languages and the class SAC 1. In this paper, we investigate the classes of languages obtained when the groupoids are restricted to be quasigroups (i.e. the multiplication table forms a latin square). We prove that languages recognized...

Subdirectly irreducible non-idempotent groupoids satisfying x · xy = y and x · yz = xy · xz are studied.

We show that Poisson fibrations integrate to a special kind of symplectic fibrations, called fibered symplectic groupoids.

We define the Zappa-Szép product of a Fell bundle by groupoid, which turns out to be over underlying groupoids. Under certain assumptions, every groupoids arises in this manner. then study representation associated with and show its relation covariant representations. Finally, we universal C⁎-algebra, C⁎-blend, generalizing an earlier result about groupoid C⁎-algebras. In case discrete groups, ...

We introduce singular subalgebroids of an integrable Lie algebroid, extending the notion subalgebroid by dropping constant rank requirement. lay bases a theory for subalgebroids: we construct associated holonomy groupoids, adapting procedure Androulidakis-Skandalis foliations, in way that keeps track choice groupoid integrating ambient algebroid. The groupoids are topological and suitable nonco...

We show that the category of internal groupoids in an exact Mal'tsev is reflective, and fact a Birkhoff subcategory simplicial objects. then characterize central extensions corresponding Galois structure, regular epimorphisms admit relative monotone-light factorization system sense Chikhladze. also draw some comparison with Kan complexes. By comparing reflections objects reflexive graphs into g...