Related papers: Partial Groupoid Actions on Categories: Globalizat…

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…

Franck Lesieur had introduced in his thesis (now published in an expended and revised version in the {\it M\'emoires de la SMF} (2007)) a notion of measured quantum groupoid, in the setting of von Neumann algebras and a simplification of…

We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories.…

We define a notion of semi-conjugacy between orientation-preserving actions of a group on the circle, which for fixed point free actions coincides with a classical definition of Ghys. We then show that two circle actions are semi-conjugate…

We establish a one-to-one correspondence between rational multiplicative group actions on an algebraic variety $X$ and derivations $\partial\colon K_X\to K_X$ of the field of fractions $K_X$ of $X$ satisfying that there exists a generating…

In this article we construct the inverse semigroup of equivalence classes of partial Galois abelian extensions of a commutative ring R with same group G, called the Harrison partial inverse semigroup.

A groupoid is a small category in which all morphisms are isomorphisms. An inductive groupoid is a specialised groupoid whose object set is a regular biordered set and the morphisms admit a partial order. A normal category is a specialised…

Through this work we introduce an action of the skew polynomial ring $\mathbb{F}_{q}\left[X; \sigma, \delta\right]$ over $\mathbb{F}_{q}$ based on its polynomial valuation and the concept of left skew product of functions. This lead us to…

Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.

In this article, we work with unital twisted partial action of $\mathbb{Z}$ on an unital ring $R$ and we introduce the twisted partial skew power series rings and twisted partial skew Laurent series rings. We study primality, semi-primality…

We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.

Let G be a group and let P be a subsemigroup of G. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a…

Proposing a certain category of bialgebroid maps we show that the balanced depth 2 extensions appear as they were the finitary Galois extensions in the context of quantum groupoid actions, i.e., actions by finite bialgebroids, weak…

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…

We bound the nuclear dimension of crossed products associated to some partial actions of finite groups or $\mathbb{Z}$ on finite dimensional locally compact Hausdorff second countable spaces. Our results apply to globalizable partial…

We study congruences on the partial automorphism monoid of a finite rank free group action. We give a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating…

Let $\Gamma$ be a sub-semigroup of $G=GL(d,\mathbb R),$ $d>1.$ We assume that the action of $\Gamma$ on $\R^d$ is strongly irreducible and that $\Gamma$ contains a proximal and expanding element. We describe contraction properties of the…

The operation of zig-zag products of graphs is the analogue of the semidirect product of groups. Using this observation, we present a categorical description of zig-zag products in order to generalize the construction for the category of…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

We introduce a generalization of the product expansion of a finite semigroup. As an application, we provide an alternative proof of the decidability of pointlike sets for pseudovarieties consisting of semigroups whose subgroups all belong…